The solution is so simple: if you do not like the PRIVATE college’s policy, do not attend it. Nobody is forcing you to attend that college. Why trample on the private college’s rights by forcing it to have these clubs against its wishes.
That's the spirit. spend a lot of time searching out schools and going through the application and admission process. Then find out as the academic year starts, the school pulls the plug on your activities. So lose an academic semester, tuition, and pick up and go elsewhere. Such a pragmatic idea. Wish I though of it.