Right now, these words have already become familiar and are the ONLY way most people can frame the argument in their heads, so unless we are only interested in discussing this with people who already have their gender studies degree, we have to communicate effectively and introduce these ideas at the rate people can comprehend them.
Barracker, I understand what you're saying and I do agree that we need to be comprehensible to people, but at the same time it's crucial that we don't use the Newspeak that TRAs have set up, because that language is deliberately designed to disappear and indeed reverse the reality of what we are trying to highlight.
Therefore we do need to pay attention to our language, being careful about what concepts we are endorsing, as theUterati said, because otherwise we aren't communicating our ideas effectively. Language is the key to this whole issue, that's why the TRAs are so militant about everyone using their terms.
Consider the difference between this sentence from the Times on Labour's AWS furore:
The founder of a crowdfunding campaign to bar transgender women from all-women shortlists has been suspended from the Labour Party
And this one from the Mail on Sunday on the WEP sacking Heather Brunskell-Evans:
The Mail on Sunday understands that the party received several complaints about the academic’s comments on the programme, including one from a man who identifies as a woman.
Notice how starkly the language in the Mail brings into view the absurdity of what the WEP - and Labour - are doing to women, and the power relations at play here. There it is, in black and white: what's going on is that women are being persecuted and hounded out of politics for the benefit of men who say they are women. Whereas in the Times article, this is completely obscured by the use of the word 'transwoman' (or worse, 'transgender women'); and not just obscured, but the power dynamics are actually reversed, with women becoming the persecutors of (supposedly) marginalised men, in the guise of 'transgender women'.
I just don't think this needs to go as far as refusing to use the word 'trans', because contra TheUterati, 'trans' is a thing, but it's a cultural thing, it's an ideological thing - hence why I use 'trans-identified' instead. That said, language that highlights the absurdity of TRA claims also works when appropriate, e.g. 'men who claim to 'feel like' women' or as per the Mail on Sunday 'men who identify as women'.