I think it's a bit silly to be making the assumption that somebody at FDEV decided to tint the Milky Way the colour of the local star. It is clearly an unintended side-effect of the new colour grading system that is very likely to be patched out at some stage down the line. But I imagine it's pretty low on the list of priorities.
HOWEVER
I can see the case for the galactic plane realistically being tinted by the colour of the local star in at least one instance - when we're close to the star itself, like during fuel scooping and beginning to move away. When we are that close to the star to gather fuel from it, we are within its envelope, and although this isn't represented at all in the game, I imagine that the "atmosphere" of the star would have a similar tinting effect that Earth's atmosphere does on the milky way.
Speaking of which, I would love for proper stellar envelopes to be put in the game - lots of the stars we come across in the game wouldn't necessarily look like perfect spheres, there are plenty of squashed, rapid spinning stars, and most of the giant ones may not even have a discernible surface.
In terms of interstellar dust; I believe the reason it doesn't look quite right is because there is a rough approximation of the distribution of the dust being generated by the stellar forge, and the skybox uses that rough approximation to build the appropriate backdrop of whichever system we're in. So, if the distribution isn't perfectly accurate, then the milky way as seen from Sol won't have the distinctive dust lanes that we see IRL. I'm not sure that this is reasonably fixable to be honest, because we only see a the dust lanes in two dimensions from Earth, but the stellar forge generates it from a three-dimensional distribution - it makes me wonder if "fixing" it so it looks right from Sol would result in a weird distribution when you move around other systems, like what happened with the 2MASS survey stars.