I don't think there's a legislative means to tone down the rhetoric other than to build anti-discrimination protection and allow the culture to catch up. And there's no "both sides" to the hate problem. The right is very proactive in having operatives come up with culture war issues to spread, starting with wing nut groups presenting to Republican governors' associations, councils, AG's, and such that then promulgate model legislation to spread the latest outrage across the country. All the anti-trans bills and the Chris Rufo CRT crap are obvious examples. Astroturfing is not a left-wing thing. And then the right-wing Murdoch and radio universe spreads the issues to the masses so the rubes see the need for all the negative legislation.
I don't believe there's an equivalent level of organization on the left, in terms of coming up with the next new champion "issue.' The left is reactive by nature -- the whole concept of Antifa exemplifies that -- because they're not the ones on the attack against marginalized groups. It's a hell of a lot easier to destroy and demonize than to solve actual problems and advance freedom without exclusion.