Cracking down on "hate speech" on a governmental level would be in direct violation of the First Amendment. The Supreme Court has affirmed on multiple occasions that hate speech is in fact free speech, there are reams of case law to support that. You as an individual have the capacity to look the other way and not listen to words you find hateful.
https://en.wikipedia.org/wiki/Hate_speech_in_the_United_States
Allowing people to express thoughts that you find distasteful, or one's you hate yourself, is the pinnacle of tolerance. Unless speech causes imminent threat of harm, it is de facto protected speech.
Designating any particular kind of speech as explicitly hateful and verboten is just a stepping stone, you're loading a gun that one day may be aimed at you. The government should ensure that all expression is protected without exception and let society figure out the rest. Private individuals have the capacity to pick and choose what it wants and does not want to engage with, social standards are malleable - too malleable to be codified in a way that would truly encompass their scope in a fair way.
Sacrificing fundamental rights on the altar of a nebulous "Greater Good" makes hair stand on the back of my neck. The "Greater Good" is like a combine harvester - it turns people who happen to be in the way into mulch. I consider the right to bear arms to be fundamental, impossible to divorce from the right to self-defense, and I weep over the fact that large swathes of the western world have been stripped of it in favour of a government monopoly on gun ownership. Defensive gun use in the U.S. is at least as common as offensive use by criminals, even going by conservative statistics.
https://www.forbes.com/sites/paulhsieh/2018/04/30/that-time-the-cdc-asked-about-defensive-gun-uses/
It's another fundamental constitutional right that should never be abridged, regardless of cost. Even if offensive gun use outweighed offensive gun use, rights are not predicated on statistics anyway - they are fundamental.