Are music and politics related somehow? Because at first you said it was a music issue, but then you said it's a political issue.

I wouldn't sacrifice a core belief just to get friends. Being grounded on something is important. Actually, I think being grounded on something is a source of self-confidence. Changing how to communicate with people is different than changing your core character. Tomorrow you will finish your PhD, and will face another group of people with other beliefs and interests. If you keep following the "majority", you will ever be following the crowd, and you will never be yourself.

Because you said you don't know when it's your turn to speak, it seemed as if you miss social cues, that's why I suspected Asperger. But I'm not a professional. If you don't miss social cues, may be it's a low self-esteem issue. I'm eager to find people to connect with, but the moment I find someone, I feel disappointed and disconnected. I'm not sure if you feel the same way.

Do you have specific traits in people with whom you want to connect with? Like education, be interested in your type of music, ... etc.