You've strawmanned the entire crux of your OP. That's not a great move. I'll try clear this up a little, from my perspective:

I suppose the super 'woke' types — unimportant

I would say anyone with eyes would agree that there is a 'too far left'. It's not serious to suggest otherwise, so that's fine.

Right wingers say they/we are just as intolerant because we don't accept their intolerance, lol — unimportant

No, they don't. They only say the first part. The second part is contingent on several things; most of all, whether what's being discussed is some form of intolerance. It usually isn't, in the 'moral' sense. We are all most intolerant of the world around us. Most things aren't what we want to be doing, or choose to be doing and we make great efforts to ensure our intolerance is maintained by not coming into contact with things we wont tolerate. I think that is uncontroversial, if a little under-observed. Now, something interesting is to figure out when "intolerance" becomes 'problematic'. Generally speaking, that's when human rights are being violated - but then, many human rights are also contingent - some (including hte UN i believe) consider internet access a human right. But taking the internet from your misbehaving child is not a form of human rights abuse, in the vast majority of minds.

My experience with the majority of right-wingers i've ever had an actual conversation with is that the things they don't tolerate are generally the aggressive, uncharitable behaviours of others. This is absolutely laden with access for bigots, granted. But absolutely so is the opposite line of trying you best to accept the aggressive, uncharitable behaviours of others as leftists like to do (there's a huge amount of social currency to getting a 'dunk' on the left although I acknowledge we have to be talking about the 'leftist' contingent and not just 'those on the left'. I'm in that camp and I find leftist thinking abhorrent). I think the issue is that in conversation right wingers don't frame their "intolerance" as reactionary - leftists do, which gives it an air of legitimacy on its face that might not be warranted - equally, the disparaging of general right-wing thinking is probably also unwarranted as it usually doens't speak to bigotries, but policy considerations.

Poisoning the well, refusal to engage and immediate labelling of views with words that justify aggresion or violence is rife on the left. These, to me, speak to a pretty intense intolerance - sometimes, of their own. There is some loose empirical data on this.

The upsurge of leftist political violence in the last two years or so seems to suggest that the left is more likely to resort to violence, albeit this is a very recent development as compared to right-wing violence. THe problem is this reflects the same disaparity as IPV does: Women (left) are more likely to engage in violence - but right (men) are more likely to kill more people per event. But stand-alone assassination attempts or successes appear to be a left-wing phenomenon.

If people could just stop for a moment, lay out their goals before speaking to their opponents, things would go much better. My experience is that the right will do this - and be respectful - where the left will not. And are usually objectively wrong about how they've characterised the point they're objecting to.

I suppose the question is what you are intolerant of, not whether you are intolerant. — unimportant

Once one sets out what they mean by "intolerance" and what counts as "more intolerant," the question becomes answerable. For example, if we take "intolerant of X" to mean "does not allow X," and we measure relative intolerance quantitatively, then we merely need to count up the different things that each group is intolerant of. Of course a quantitative analysis will probably be insufficient, but you get the idea.

A core problem on the left is actually an equivocation where they want "tolerance" to mean "acceptance." Once one recognizes that tolerance does not mean acceptance, and that tolerance implies dislike or aversion, much of the muddle coming from the left dries up. The critique from the right is basically a request that the person on the left actually survey the things they are intolerant of, instead of pretending that they are "tolerant" of everything and that it is merely a matter of the tolerant vs. the intolerant.