Maybe, but gender and sex mostly align, and it certainly has to be about sex, and making it about gender to counteract the gender-or-sex-based-dismissal is the only thing that's really worked.

In light of that, I would expect a great deal of sensitivity to anyone who feels uncomfortable changing the language.

Also, the stuff about contexts where it is important is really not true from what I've seen. Nobody backs off when the inclusive language actually impedes clarity and precision, and it's often used where the context actually isn't very important, just plausible. For instance, I have seen scientific studies where it would be insane to average trans men into the woman group because the hormonal differences would swamp whatever was being studied. If you read the methods, you find that because the authors aren't stupid, they didn't average them together and in fact they had zero trans men at all because it's impractical to get a large enough sample size for most studies and so they were one of the categories excluded...except they still use the "inclusive" impersonal language everywhere, making it hard to tell what actually happened. As another example, I've seen cases where medical advice is just rewritten to use inclusive language but without re-evaluating whether all the advice actually makes sense for someone who might be taking testosterone supplements. This could even be dangerous to anyone who isn't getting appropriate personalized advice from their doctor, but mostly just isn't appropriate. For instance, as a cis woman you should be rather alarmed if your menstrual cycle becomes irregular and infrequent (unless you're approaching menopause)...but not if you're a trans man taking testosterone.

If we're going to use inclusive language to be inclusive, I wish we'd just be honest about it. And be gentle with people who don't instantly feel comfortable being talked about as body parts.