I experienced this the other day. The argument was about the rules for who can be US vice-president. One side was using the US constitution as the ultimate decider. The other side was using a French 14 hundred definition of who can be vice-president. This was in the US. These types of arguments are happening regularly. If people are picking their own rule book, how can we ever come to an agreement?
Yes, language is an issue. Unfortunately, and ironically in the context of the OP, the majority of issues worth discussing can't even agree on what the root problem is. Instead, the conversation market gets flooded with distractions, symptoms and/or false god narratives. From there it's off to the world of binary and confirmation bias.
Rinse. Repeat.
Meanwhile, the entities responsible and accountabile for the root problem(s) get a free pass.
That's a step past language. You're not listening. You're not even pretending to listen. Trans people have a real life experience and you have no interest in it. You want to tell them what to do and not a single word they've said crosses your ears.
We can't have language issues when there isn't even hearing.
Yes, a very good example of a space of discourse it's extremely hard for people across a divide to discuss dispassionately, or in the same language, due to variances of meaning and intent behind use of words.
CSAM and cryptography has risks of heading the same way.
Before the trans gender issue of course we had (and continue to have) this problem in women's reproductive health and abortion rights. "Right to life" being a phrase devoid of literal meaning before the debate, it became captured by one side to refer to a specific thing.
Trans exclusionary radical feminism seems to me to be a tolerably clear concept at least. Arguably, it's no different to statist or libertarian, "radical" aside it carries little stigma. TERF as a term of abuse is just an objectifying label. I've always suspected that the "radical" word was put in to objectify a sub group of women.
Dale Spenders's book "man made language" comes to mind.