(And on the other hand, not tolerating these ideas also opens the door to making other beliefs shared with any of these belief systems taboo.)
I don't think that is a very useful definition of tolerance. The only stable system here, if there is one, might be something like hardcoded self-defense actions, plus otherwise general tolerance. Not saying it's logically or morally consistent.
I feel like I've often heard the paradox of tolerance invoked in regard to what U.S. free expression law would call "pure speech", but it seems like your point is more along the lines that there's no group or society that would literally do nothing at all to defend itself in any circumstances, and that that's an unachievable or unsustainable extreme. Maybe something like the most extreme form of pacificism, where people imply that they will literally allow themselves to be killed without trying to prevent it in any way.
Second, I think of tolerance as a personal thing. But on a level of society or government, that you're talking about - I don't know, you tell me.
Let me ask you, do you tolerate sexist jokes? Because I really doubt many of the today's proponents of this theory do. Sexist jokes are not intolerant, making them is not an attempt to overthrow any kind of system, it's just jokes. But yet, a lot of people do not tolerate them. Either don't want to be in the same room as the person who makes them or will even try to harm this person in some way. Both fit the definition of intolerance. Former is completely fine, latter probably not so much.
But as I understand it, it's not so much about petty things like this, but about intolerant ideologies. Well, communism happens to be one of those ideologies. It does not tolerate anyone who owns or argues for private ownership and seeks to overthrow any system that protects it. And if we were honest, that would mean that we should also get rid of a large part of Antifa (ironically a manifestation of this theory), because many of them self-identify as communists or subscribe to ideologies derived from it.
> Where do laws fit in here?
Speech laws, freedom of association. Criminal law in case a real harm was done. The word "tolerance" should not appear anywhere in the law.