"can a hate message be peaceful?"
This is an excellent moral/ethical dilemma which I don't think I can truly answer. For the purposes of the First Amendment and the purposes of "protesting" I think the answer is yes. When BLM was protesting, several of their chants were "hateful", even threatening towards police.
One of their worst was "Pigs in a blanket, fry em' like bacon"
That chant meets your argument of "hate message" but was considered acceptable by the left. (Even defended) Only one of the racist chants I heard on the news hold a candle to that imo. (Much of the crap spewing out of their mouths as individuals was worse though.)
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If we silence these people now, where does it stop? I think next on the list would be religious organizations that are against homosexuality. Laws need to be applied to everyone equally and shouldn't be revocable when its convenient to a majority.
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We should condemn their ideology through starvation of attention, not silencing them.