How to politely tell someone what they are wearing doesn't look good on them without hurting their feelings
You don't. This is your problem, so deal with it, no need to involve the other person. This person is "disagreeing" with one or more of your values, and you're upset with them. Why is it their problem?
"Deal with it" means getting to grips with your motivation for assaulting another person with your judgement(s). Lack of acceptance, superiority, need to e right? It won't be pretty.