Rather than being sensitive about the feminist label applied to oneself, how about instead just being a normal human and talking. Maybe we'll agree or disagree on things, and I will be polite and respectful regardless. But I am not going to walk on eggshells to make sure you don't feel offended or judged-if you're an adult, handle your emotions, they aren't mine to deal with. When you identify with a label, you reduce yourself to a caricature. I don't waste time on caricatures. I don't waste time on people who are overly sensitive about their own views. And you're paying your half of the bill.
You know the saying, "what happens in Vegas stays in Vegas". Whatever your partner says during a fight should stay there. So if they say something during the fight that bugs you, tell them their words are frustrating you.
HOW LONG AFTER HIS BREAK-UP SHOULD YOU WAIT BEFORE DATING HIM???
If their fighting words annoy you the next day, give yourself some breathing room instead of approaching them again so soon. Bringing up an argument too often can lead to talking in circles, not a resolution.