Re: Would you support the government pursuing hate groups as they do terrorist groups
White Nationalist groups, KKK, New Black Panthers, Conservative Citizens, Aryan Nation, or any other groups that promote hate and encourage others to perpetrate hate against others.
I may not be asking this the right way.
I am asking you to define "hate" in a manner that would equate to enforcement of some law, and would not be a violation of the 1st Amendment.
At present you have a constitutional right to say plenty of terrible things about someone, or some demographic. It becomes "hate speech" the moment you "incite violence or prejudicial action" against someone (usually in the context of a legally defined protected individual, group, etc. Breaking civil rights law, something along those lines.)
All the groups above exist presently, and even though I am sure they are watched what they print and say about someone (or some group) is protected *until* they advocate some violent act or purposeful breaking of law.
The way you have phrased the OP, my answer is no.
The whole point of the 1st Amendment, in this context, is protecting the freedom of speech. I would agree you are responsible for what you say and that includes the element of inciting violence. You do so, you are subject to consequences. As a product of our rights it means hearing things you will not agree with, perhaps even be disgusted by.
Our issue is once you remove the incite violence or breaking some law qualifier, then all "hate groups" become is whatever political will defines hate groups to be. Take modern liberalism, who often defines far right wing rhetoric as hate speech and inciting some level of concern for governance. If we go down that road then hate speech and hate groups is nothing more than a moving target purely subjected to majority power political whim. At that point, any group could be considered a hate group. Then we have major issues, freedoms lost.