Obviously you have to be flexible and not push things; say they get really offended anytime you say "banana" ; you might think "that's fucking stupid and illogical" but still you should refrain from saying banana, you can't try to reason with them about the unreasonableness of their offense. You have to just respect it and let it go. Say you really like musical theatre, they don't, so don't try to force them to go to musical theatre. And they also have to be flexible and understanding enough to let you go to musical theatre on your own in that scenario.
A crucial aspect is being sympathetic. You have to care about their feelings and sympathize even if you think they are being illogical or unfair or whatever. I find that whole "I hear that you are saying you feel insecure because of the way I looked at that other girl" kind of repeat-back mantra to be really repulsive since it's just a surface act, maybe it helps, I dunno, but the real thing you have to do is much deeper. You have to actually care that you hurt them and not care why, even if you think they are being totally unreasonable, you have to try to see the way they are experiencing the situation and how you can make it better for them.
One of the hardest moments is when you do something that hurts your lover and they lash back at you. In this moment they can say things that are really hurtful, because they know all the things you are most sensitive about, and also because coming from their mouth it stings doubly. The ideal response is to ignore their words (since they didn't really mean them) and hear what they are really trying to say which is something like "you hurt me", and try to stop yourself from responding with anger and instead look at what you did that made them act that way. This can be very hard to do in practice, it requires great levels of self control and confidence and awareness.
Something I always struggle with is the idea of "fairness" (like wah wah it isn't fair). You feel like you are putting in all this work and the other person isn't matching, or you feel like you're compromising more than them, or you're doing so much and they don't appreciate it or whatever. You feel like they're mad at you and they don't have a good reason to be; "wah wah it's not fair, I've been so good". You feel like they should suffer as much as you. Or you know that you could smooth over a fight by compromising but you don't think they've earned the happiness that you can give them. It's important to get past all of these ideas. For one thing, you may well be wrong - it's easy to see the work you are doing, it's not always easy to appreciate how much the other person is doing for you, so your idea that you have been compromising more might just be total hogwash. For another thing, even if you have been doing the lion's share of the work, so what - if you can make the situation better, you should do it, because you should be working with your partner for improved joint happiness. There's no contract that you both have to put in the same amount of work; it's really hard not to hold a grudge about this; in the extreme case maybe your partner puts in hardly any work at all and you do all the comforting and compromising, outside observers might call you a "sucker" but if it is a pathway that leads to your joint happiness, then it's the right one.
That said, you don't want to just eat abuse. Sometimes your partner just serves you a shit sandwich and you don't want to eat that over and over. I'm still really not sure how to handle this situation. Sometimes there's an excessive tendency of the mature sensitive male to always find blame in himself. That is, once you reach the awareness that you are working towards joint happiness and that your actions are always part of the puzzle, you start thinking, oh this situation went really bad, what could *I* do better next time, or what did I do that caused this? Certainly that's a good line of thought, and you should pursue it a bit, but you can go too far and just degenerate into martyrdom.