That just isn't true. The Boy Scout policy that you - and Berkeley don't like - is a form of free belief and free speech, so recognized by the Supreme Court. Berkeley can't discriminate against the Scouts because of what the Scouts believe and what they say.
So the fact that other groups believe differently, and therefore get the subsidy, while the Scouts are denied the subsidy because of their beliefs, is discrimination that violates the First Amendment.
Berkeley could cut off all subsidies to everybody - - that would be fine, since it doesn't have an obligation to provide subsidies. But it can't withhold subsidies selectively because this or that group holds beliefs, and policies based on those beliefs, that differ with Berkeley's official beliefs as expressed in its antidiscrimination rule.