Then we are both in agreement that this is the silencing of speech by the state.
One doesn't need to agree with these protesters to understand that they are calling for what they consider to be moral treatment and non-discriminatory policy. If redressing your state for what you think is immoral and discriminatory isn't protected then what is?
A question for you. What is your opinion of homosexuality?
Is it right or wrong? Moral or immoral?
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What they're "asking for" is immoral.