The binary stars system is comprises of a red giant with 6 solar masses and a Sun-like star, the exoplanet is orbiting in the Goldilock's zone with a molten iron core which generate a magnetic field similar to Earth. My question is would the strength of Earth's magnetic field be sufficient enough to block the deadly solar wind to allow intelligent life to exist? (Treat the exoplanet like Earth.)
This system won't have been around long enough for intelligent life to evolve, if Earth is any guide.
Big stars burn fast and die as supernovae. A red giant represents its death throes, and this system has only a few million years left ( if that)
But since it is a binary system, not a separate solar system that has strayed far too close to a red giant for its own good, we can deduce that the star and the planet formed at the same time as the six solar mass star. Therefore, nothing except primitive life will be there.
EDIT see comment, no supernova, 6 Solar masses not heavy enough. But this system will nevertheless be far too young. The red giant will be a white dwarf well inside the first billion years.
Since you said that the smaller, brighter star has a habitability zone, the red giant is not preventing that. The two stars therefore orbit each other at a much greater distance than the planet and the brighter star.
If the exoplanet's magnetic field is sufficient to protect it from the nearer, hotter star, all is well as far as the larger and more distant star is concerned.
Your star would be no more than 20 million years old if it was born at the same time, so it is unlikely that there would be life on it, but it is possible that the Red Giant caught the yellow dwarf later in life. The problem is that it would be less than 20 million years ago, there likely would be a mass extinction around that point, and the red giant is likely to eject it's mass soon and destroy whatever life is there...
Supposing that isn't an issue you're dealing with 2 solar winds which means 2 times the radiation get through which should speed evolution by a factor of 2 which means it should recover enough to have sentient life on it if that's what you're aiming for. You just have to have the Yellow Dwarf and planet orbit far enough away from the Red Giant. Of course points in the orbit that are closer to the Red Giant would be hotter, but other than that i don't see any major problems save for the impending death just on the horizon for these people...