I get pissed of about both of those things too. the first one comes up a lot lately, I swear I say 'I can do whatever a cisguy can do and still be a guy' at least once a day (maybe I'm exagerating a little but still...). But the second one annoys me the most, sorry but if you can't give me the most basic forms of respect I'm not going to spare you either.
I had a very specific situation for years with my close family about some other familymembers (not really though, I don't consider them family) who treated us terribly, but I had to be nice and normal if we saw them for years. I guess maybe that's why I'm so sensitive to the 'you be the better person' line. I had to be nice to those people simply because my mom was worried others would think me rude... Recently we have agreed to disagree and she's even said she was kind of jealous that I could react the way I wanted. So progress is being made

The freedom of opinion/speech thing has bothered me for years, it doesn't mean that you a) can say whatever you want and be rude and b) are free from other opinions and criticism. You want to spout your opinions, you better learn to deal with mine! Also I don't really believe in the 'if you ignore them it will pass' idea, my experience is that a nice clear 'You don't get to mess with me' message works better then ignoring. Also it makes me feel a lot better if I say something then if I just endure it all. Sometimes just letting people continue gives them the message that it's okay to do that.
The caring thing is an issue. I care far too much sadly. I've sort of stopped tring to stop caring, I'm afraid I'll never get there anyway. I just allow it to hurt for a moment, but try not to let it influence how I end up acting. And I try to act up, because as I mentioned earlier that helps me. Knowing I did something about it, and then trying to let it go. And, this may be weird, but I practice 'being me' with my friends. I'll be going to my supportgroup in kilt on saturday, just because I want to and like it, and I kind of want to get more positve experience being totally me. I am lucky however to have this small amount of people where I can practice.
(sorry for wall of text and possible irrelevance

)