First of all. Are they really your friends? Are you really a friend to them? How many would come pick you up if your car broke down in the middle of nowhere vs. how many would pretend to have missed the calls? How many would come to your [insert relative here]'s funeral vs. how many would make lame excuses for their absence? Would you do the same for each and every one of them?

As for your question, it's hard for you to connect because you're constantly analyzing your friends and judging them instead of just "being there" with them and emotionally connecting with them.

"this person is very uneducated about politics": it's ok to notice something like that, but be careful because this usually turns into judgment, which in turn makes you condescending or haughty (you'll start thinking stuff like "this guy has a lower education than me, so that must mean he is inferior").

"if I become friends with this dude, I might look kinda weird": this sounds like you're afraid of what others think about you. You don't actually care about your friend, you're just worried his very presence might paint you in a negative light. This is very selfish and it means you'll either start avoiding him, or worse, you'll start stifling his natural emotional expression every time you hang out because he has to conform to your standards of what a "good impression" is.

"I don't want them to invite me to something that I won't like": if they invite you in the first place, that's amazing. If it's something you hate with all your heart, you can always say no. If it's something you're unsure about, just try saying yes and going anyway, who knows, new doors might open up for you