I'm in a similar boat to yours. On my mother's side of the family (very large extended family) the mentality is that they freeze out anyone who doesn't fall in line. It's like a gang mentality.
After a lifetime of it, I stopped putting up with my parents' abusive behavior two years ago and stopped talking to them. Before that time, I was casually friendly with many of my cousins. Immediately, upon stopping contact with my parents, my cousins stopped responding to my emails and attempts at contact. Before that, they were happy to visit with me. They had witnessed how my parents had treated me, but it was "faaaamily" and I was supposed to just shut up and be miserable (aka "out of respect for your parents"). All this, even though my cousins also always avoided my parents and our relationship was separate from one with my parents.
None of them told me "I'm avoiding you until you're in your parents' good graces again." They just didn't reply to me. Of course, I was upset. But then I had to be honest with myself that most of those relationship I wouldn't have had had we not been related in the first place. And I had to remind myself that even in the old circumstances, I was still the one doing the bulk of the work in the relationships, extending most of the invitations, etc. I had very little in common with these cousins to begin with. It stunk realizing that I was not someone they valued spending time with. Their relationship with me was completely contingent upon my remaining a doormat to my parents.
I have a couple of cousins who have stayed in touch with me despite this. The rest generally don't contact me and I don't contact them. After a year or so of them all giving me the silent treatment, a few started emailing me and saying "I don't know why you're mad at me" or "we miss you." But they don't miss me because I am fun, smart or interesting. They miss their doormat. And I'm not interested in their fake version of a relationship. I have better things to do with my time.