Intolerant: disapproving of or refusing to accept ideas or ways of behaving that are different from your own.[2]
These are the definitions from Cambridge Dictionary and show these words are direct opposites of each other. We can look at it like boolean logic.
True == !False
!True == False
NULL != True
NULL != False
NULL != !True
NULL != !False
Tolerant == Not Intolerant
Not Tolerant == Intolerant (the literal definition of the word)
NULL != Tolerant
NULL != Intolerant
NULL != Not Tolerant
NULL != Not Intolerant
The Musk example is not "not tolerant". It is NULL. It is making no comment about Nazism. The Babylon Bee article was not a NULL value because it was directly commenting on the acceptance of trans people.
[1] - https://dictionary.cambridge.org/us/dictionary/english/toler...
[2] - https://dictionary.cambridge.org/us/dictionary/english/intol...
A possible alternative position is tolerance for others' words and definitions, and this was the mainstream progressive position up to about 10 years ago.
That is not using your creative definition of the word tolerance, but the common one and the one which was used by progressives when they advocated for that position. So there's an answer for your question I originally answered.
But I am glad you have understood that a comment is not necessarily tolerant or intolerant. That's great progress, it took a while, but I applaud the effort and persistence. Good luck with the rest of the journey.
That is absolutely not the heart of the disagreement, just a weird definition that you're wrong about. The disagreement is fundamentally about whether tolerance for speech means allowing people you disagree with to speak.
Tolerant means you are tolerant toward others. Speaking is not itself an act of tolerance toward other people. I could make a post about Linux programming on Hacker News, that would not be tolerant toward trans people for example. It wouldn't be intolerant, it's just that it wouldn't be tolerant because I am not "tolerating" anybody when making such a post.
Or let's take another example in the strange gotcha twitter style you seem to be most comfortable communicating with: You posted an earlier comment which was "Yeah, insiders not knowing the full details of Musk's plan because Musk doesn't have a detailed plan yet seems more likely than WaPo just making some stuff up." There was nothing in that comment that showed an intolerance to Nazis attacking Jews, so you saying that you you are tolerant of Nazis attacking Jews when you made those comments, right?
There is nothing about the in- prefix of the word or anything else about it that means everything must be either tolerant or intolerant, that's ridiculous. Insoluble is the opposite of soluble, meaning it can't be dissolved. Does that mean your comment is insoluble because it is not soluble??