Maybe you should forget about the color of the sky of your planet, and wonder whether your planet could possibly have most of the things which make a planet interesting for a science fiction story.
If your planet is supposed to have an unbreathable atmosphere of nitrogen and carbon dioxide, for example, and the humans all wear spacesuits or at least oxygen masks when outdoors and live in airtight communities, having a red giant and white dwarf star in the system is fine. The Humans can be on the planet for mining, and/or to study the primitive single celled lifeforms that don't require an oxygen atmosphere since they don't breathe, or for some other reason.
But if you want humans to be able to breath the atmosphere of the planet, or there to be an alien civilization on the planet, or for there to be large multi celled plants and animals on the planet with biochemestry similar to that of Earth multi celled plants and animals - in short, if your planet is a typical science fiction planet where interesting things can happen - then your planet can not have stars of any imaginable type. There will be strict limits to the types of stars that will be possible in your star system.
Most discussions about planetary habitability discuss whether a planet could be habitable for any one type of life on Earth, not whether that planet would be habitable for every type of life on Earth.
I note that if a human was magically transported to a randomly chosen location within Earth's biosphere, they would almost certainly die, since Earth's biosphere extends for kilometers or miles above and below the surface. And if a human was magically transported to a randomly chosen location on the surface of the Earth, which is a tiny fraction of the total biosphere of Earth, that human would still probably die.
About 71 percent of Earth's surface is ocean, where a human would soon die. Much of the land surfaces are hostile deserts, or ice, or barren lands without food edible for humans. There is life all through Earth's biosphere, but humans can survive in only a tiny fraction of Earth's biosphere.
What science fiction writers need is a discussion of alien planets which are habitable for humans, or for large multi celled land dwelling oxygen breathing animals with requirements similar to those of humans.
And there is such a source, Habitable Planets for Man, Stephen H. Dole, 1964, 2007.
Dole points out that it took Earth literally billions of years to develop an atmosphere with a lot of free oxygen breathable for human. That oxygen was produced by plants through photosynthesis. So life existed on Earth for billions of years before it produced an atmosphere breathable for humans and thus became habitable for humans.
So Earth had to have life flourishing for billions of years to become habitable for humans. And that life could only flourish if Earth's temperatures didn't change wildly over that time, killing off the life. So that means the Sun had to have a fairly steady luminosity for billions of years, otherwise Earth's temperature would have changed too much and life would have ended before producing an oxygen atmosphere.
Dole estimated that a star would have to remain on the main sequence and shine rather steadily for at least two or three billion years in order for a planet to develop an oxygen atmosphere and become habitable for humans. And that was being rather generous since Earth and the Sun existed for about four billion years before Earth became habitable for humans.
In Chapter Four "the Astronomical Parameters", in the section "Properties of the Primary" Dole considers what types of stars are suitable for having habitable planets. They have to be stars during the main sequence part of their life cycles, since once stars pass their main sequence stage their planets are extremely unlikely to remain habitable, if they are not destroyed.
When a star leaves the main sequence stage, it swells up into a red giant stage, becoming much larger and many times more luminous than it was before. The increased radiation from the star may boil away the oceans and strip away the atmospheres of its closer planets, and possibly vaporize those planets. The expanding star may swallow its closest planets. A star might expand into a red giant, shirk to a smaller size, and expand to a red giant again several times.
At the end of this process the star will usually eject a lot of its mass, which is likely to be very damaging to its remaining planets. And some stars will eject their mass with a nova or supernova outburst, which is likely to really damage their planets or perhaps totally vaporize them.
And at the end of those processes the star will shrink down to the final stage of its evolution. For most stars that final stage will be a white dwarf star, but for more massive stars it will be a neutron star, and for even more massive stars it will be a black hole.
In my fictional binary system, my planet has two suns: a white dwarf star and a red giant.
And as I just pointed out the red giant star and the white giant star have already passed through the stages of their lifetimes when they had fairly steady luminosity and life could exist on their planets for possibly billions of years, possibly long enough for those planets to produce oxygen rich atmospheres and become habitable for humans and similar beings.
Now the red giant star has become many times more luminous than before, and any of its planets which were habitable for humans, or had any type of life, before, would have been roasted and rendered totally uninhabitable, and might have been swallowed up by the expanding star. Some of the outer planets and moons of the red giant star may now be at the right temperatures for Earth life, and life may exist on them, but those world should not be at the right temperatures long enough to develop oxygen atmospheres and become habitable for human like beings.
And the white dwarf star has already done that. It has already roasted and maybe swallowed its inner planets, and perhaps warmed up its outer planets so they were warm enough for life, and then shrank again, so the outer planets froze over and all life of them died. And the white dwarf star might have already become a nova or a supernova, and might have vaporized all its planets, and maybe vaporized all the planets of the red giant star as well A supernova, for example, would be way to violent for any solid matter in the same star system not to be vaporized.
It would be possible for a super advanced alien civilization to terraform planets orbiting a red giant or a white dwarf star, perhaps moving them from their original orbits to orbits where they have the right surface temperatures, giving them oxygen rich atmospheres, etc. Those super advanced aliens might consider it worthwhile to take thousands of years to terraform planets in return for those planets remaining habitable for millions of years.
And as far as I can tell no story with a habitable planet in a binary system containing a red giant star and a white dwarf star can be scientifically plausible, unless a part of the story line involves that planet having been terraformed to become habitable by a highly advanced civilization.
If you want your planet to be naturally habitable, you should replace the white dwarf star with a main sequence spectral class F star, which will be a bit whiter than the Sun, and replace the red giant with a main sequence spectral class K or M red dwarf star which will be a bit more red than the Sun.
I can not calculate what colors the stars will appear to be, especially though an atmosphere, but if someone sees them side by side in the sky they should be able to tell they are different shades. Objects will definitely look different shades in the light of one of the stars than in the light of the other star, but I don't know how big the difference will be.
You describe the two stars of the system as suns of the planet. A star can be considered to be a sun of a planet if it at least sometimes appears large enough in the sky of the planet to have a visible disc, instead of appearing as a dimensionless dot of light.
A typical human can see an object as a disc instead of a dimensionless dot if it has an angular diameter greater than about one arc minute. One arc minute is one sixtieth (0.01666) of an arc degree, which is one three hundred and sixtieth (0.002777) of a full circle. Or to put it the other way, an arc degree is 60 arc minutes, and a full circle is 360 degrees, thus making 21,600 arc minutes in a full circle.
So if an object has an apparent diameter of one arc minute, a full circle around the observer to the object will be 21,600 of that object's diameters in circumference, and thus that object will be at a distance of about 3,437.7496 of its diameters.
Since the Sun has a equatorial diameter of 1,391,400 kilometers, it should appear to be about one arc minute in diameter when at a distance of about 4,783,284,793 kilometers, or 31.97428 Astronomical Units (AU). And the largest star with a habitable planet should probably have no more than 1.5 or 2.0 times the diameter of the Sun and have a visible at no more than 1.5 or 2.0 times that distance.
The smallest stars have diameters only about the same as that of Jupiter, which has a diameter of about 142.984 kilometers. So a tiny star with the same diameter as Jupiter should appear to be one arc minute in diameter when at a distance of 491,543,188.8 kilometers, or 3.28576 Astronomical Units (AU).
So if there are two stars in your fictional star system, your habitable planet could orbit either one of them, or orbit both of them if they are close enough together.
If a star orbits only one star in a binary system, and the other star is at least several times as far away as the planet's orbital radius, that is called an S-type orbit.
If a planet orbits both of the stars in a binary system, that is called a P-type orbit.
Depending on the masses of the two stars in a binary system and the distances between them, it may be possible for stars in S-type or P-type orbits to orbit in the circumstellar habitable zone, and thus have temperatures suitable for life, and also to have orbits which will be stable for billions of years. Or, depending on the the masses of the two stars in a binary system and the distances between them, it might not be possible for planets in either S-type or P-type orbits to be habitable.
In non circumbinary planets, if a planet's distance to its primary exceeds about one fifth of the closest approach of the other star, orbital stability is not guaranteed. Whether planets might form in binaries at all had long been unclear, given that gravitational forces might interfere with planet formation. Theoretical work by Alan Boss at the Carnegie Institution has shown that gas giants can form around stars in binary systems much as they do around solitary stars.
Studies of Alpha Centauri, the nearest star system to the Sun, suggested that binaries need not be discounted in the search for habitable planets. Centauri A and B have an 11 au distance at closest approach (23 au mean), and both have stable habitable zones. A study of long-term orbital stability for simulated planets within the system shows that planets within approximately three au of either star may remain stable (i.e. the semi-major axis deviating by less than 5%). The habitable zone for Alpha Centauri A extends conservatively estimated from 1.37 to 1.76 au2 and that of Alpha Centauri B from 0.77 to 1.14 au2—well within the stable region in both cases.
For a circumbinary planet, orbital stability is guaranteed only if the planet's distance from the stars is significantly greater than star-to-star distance.
The minimum stable star to circumbinary planet separation is about 2–4 times the binary star separation, or orbital period about 3–8 times the binary period. The innermost planets in all the Kepler circumbinary systems have been found orbiting close to this radius. The planets have semi-major axes that lie between 1.09 and 1.46 times this critical radius. The reason could be that migration might become inefficient near the critical radius, leaving planets just outside this radius.
For example, Kepler-47c is a gas giant in the circumbinary habitable zone of the Kepler-47 system.
If Earth-like planets form in or migrate into the circumbinary habitable zone they are capable of sustaining liquid water on their surface in spite of the dynamical and radiative interaction with the binary star.
The limits of stability for S-type and P-type orbits within binary as well as triple stellar systems have been established as a function of the orbital characteristics of the stars, for both prograde and retrograde motions of stars and planets.
So you can have your habitable planet orbit in the combined habitable zone of both the stars, the larger type G or type F star and the smaller type M star. At he distance of that habitable zone both stars would appear as visible discs or "suns" in the sky of the habitable planet.
Or you can have your habitable planet orbit around only the larger type G or type F star. That star will appear as a disc and a "sun" in the sky of the planet. The smaller type M star would orbit at least few times farther away than the planet's orbit, and so might appear as a tiny disc or "sun" in the sky of the planet or as a dimensionless dot of extremely bright light.
Or you could have your habitable planet orbit around only the smaller type M star. That star will appear as a disc and a "sun" in the sky of the planet. The larger type F or type G would orbit at least few times farther away than the planet's orbit, and so might appear as a tiny disc or "sun" in the sky of the planet or as a dimensionless dot of extremely bright light.