For Average Joe, it is probable that "liquid" means "I can swim in it". That means that you can actually push the liquid away to make yourself move, by conservation of momentum.
So your liquid needs to have a mass. That yields several problems :
If the liquid have a mass, it is attracted by other massive objects such as star. In order to still fill the whole universe, and not just be aggregated around stars (or at a larger scale around galaxies), it needs to be incompressible. At the same time your liquid must dilate as the same rate as the universe to always fill it (but I will not address this problem in my answer).
Planets moving through the liquid will push on it. Therefore, a planet is slow down by the liquid except if both travel at the same speed. That implies currents in the liquid. That kind of system could be stable only if there is no friction, otherwise the currents will slow down, and thus the planets. It would leads to the planets simply falling into their stars (and stars falling on the centre of their galaxies). So, your liquid needs to be frictionless.
A partial conclusion is that you need a massive, incompressible and frictionless liquid. It does not looks like a big deal at first, but in fact it is.
The problem is for the liquid to be incompressible. When you push on a liquid in real world, you create a compression wave in it, and since the compression/decompression process travelling in the liquid takes time, the wave propagate at finite speed (the speed of sound in the medium).
However if the liquid is truly incompressible, the wave (i.e. information) will travel instantaneously, thus faster than light. Breaking relativity is probably not a good start.
It is possible that due to this, any push on the liquid will leads to the displacement of an infinite amount of mass (and therefore being impossible), but I have not yet figured it out in details.
In conclusion, to looks like a liquid for Average Joe, your interstellar liquid needs to breaks some laws of physics. Indeed, in our world a incompressible frictionless liquid is not possible. And this breaking leads to even greater breaking of physics, at least relativity, but it is hard to figure out exactly how much you will have to break.