how can a characters pronouns matter this much
They matter jackshit, but if one small group of lunatics for whatever reason tries to push a "Yamato is transgender" agenda - which is just objectively wrong - people rightfully get mad.
When this small group of eliticist lunatics continues to double down and act all smug and toxic despite every single evidence being against them, you get the Yamato situation we ended up in.
It's their fault and their fault alone, despite what conspiracy theory they're coming up with.
Just look at Kiku - nobody got any problem there.