The problem that opens up is the definition of intolerance. Are direct claims against the rights of others to believe something intolerant? Yes, they probably are. What about speaking against groups of people (in a broad sense, calling out some perceived problem with their behavior)? Well, sometimes that's intolerant, sometimes something needs to be said (maybe that group is the Inner Party and they're taking too much). What about speech that doesn't directly disparage anybody, but that makes certain people feel incredibly uncomfortable and unwelcome? Well, that can be exclusionary, but everything makes someone uncomfortable. (some Christians might not want you bringing evolution in to schools (which they perceive as just another competing ideology), and some trans people might not enjoy being picked apart in critical gender discussions everywhere they go. The reader might agree with one of those two but probably not both.)
So, as you can see, it's really a microcosm of the idea that "we should support good and ban evil."
Agreed. I think the solution is to really pluck at those grey areas, as of course it's easy to work in black and white. To generalize, I think the general best course is to first understand why the intolerance exists, its validity, and then address it from there in ways still consistent with tolerance. Easier said than done of course, but I'm not intending to write a philosophical dissertation here fully.
As a reminder that many who likely support this view need, you should be intolerant of intolerance, not people who hold intolerant beliefs or practice intolerance.
> ...not people who hold intolerant beliefs or practice intolerance.
The problem is that we've done a splendid job blurring the lines between identities, beliefs, speech, and behavior. We have no ground rules for how to be intolerant of some things without seeming intolerant of the people that care deeply about those things.
But we now we need a framework for defining what good and evil are. Some people defer this to their religion, while others take other philosophical avenues. Nietzsche’s perspectivism comes to mind here.
So, as you can see, it's really a microcosm of the idea that "we should support good and ban evil."