à étoiles multicolores

If you're not talking about specific stars, you omit the article. Without it, the reference is to stars in general.

So why do we say "tarte aux pommes"?

You know better than to ask too many "why" questions, Alan. It's a language.

Well, your answer was to a "why" question, but I suspect that the use of "à" in one case and "aux" in the other are both just idiomatic. 

With "de" and "des", there's a distinction between general and specific in many cases, but I'm not convinced there's a similar pattern with "à" versus "aux". 

Not directed at Alan, but shared as a personal experience for everyone getting frustrated with those difficult to remember rules and their countless exceptions:

In general, trying to find rules and reasons for everything when learning a language leads you down the garden path. The mindset you find yourself in is not conducive to learning the language on a fundamental level. You'll get frustrated quickly. And, let's be honest, most reasons given are really just renditions of "that's just the way it is" ("idiomatic" is a dead giveaway). Asking "why" acts like a filter for your brain: you condition yourself so that the fact will only be accepted and internalized if there's a suitable reason for it.

A child learns a language without even once popping the "why" question. Sure, adults learn a language differently from a child. But in the vast majority of cases it is better just to smile, close your eyes, and repeat the sentence or phrase a couple of times to let it sink it. Your brain will find a place for it. And soon you'll have internalized it.