The credibility of a view is not affected by who endorses it - so the fact many sexists endorse subjectivism about sex isn't, in itself, evidence that the view is implausible.
So ignoring entirely who does and doesn't endorse it, is subjectivism about sex at all plausible? I think the answer to that is a pretty clear 'no'.
There are a variety of subjectivist positions available, all quite implausible.
For example, the view that you are sex X if you think you are sex X is incoherent. For thoughts have content, and so the thought that you are sex X needs to have some content - that is, the thinker needs to be thinking something. What are they thinking when they think they are sex X? Well, whatever they are thinking - whatever content their thought has - will express a view about what they think being that sex involves. And thus it will involve more than just 'thinking' you are that sex.
So that view - you are sex X if you think you are sex X - makes no sense and can be dismissed as incoherent.
Then there's what we might call the 'performative' view. A performative is where you make something the case by doing or saying it. So, "meeting adjourned" is a performative. For saying it will - if you are the chair - adjourn the meeting. Likewise "I promise to pay you $5" makes it the case that you have promised to pay $5. Sometimes, then, saying something makes it so.
Some subjectivists about sex take this idea and apply it to sex, arguing that sex is a performative (or that 'one' way in which you can qualify as a given sex is by performing a performative). Saying you are sex X is a performative (it is argued) and so just as saying "meeting adjourned" adjourns the meeting, so too saying "I am sex X" makes you that sex.
This view is not incoherent, but it doesn't seem to have anything to be said for it. Why on earth think sex is a performative? The brute possibility that it could be? That's not a good reason in any other context (the brute possibility you are a murderer is not good reason to think you are one). And in other cases of performatives - promises, marriages, meeting adjournments, pardons and so on - it is intuitively clear to virtually everyone that the saying of the thing makes it so. If being sex X is something that can be achieved via performative then we would expect it to be obvious to most reflective people that it is - that is, that saying "I am sex X" is away of becoming sex X. Yet it is far from obvious as the existence of heated debate over this matter testifies. And thus there just seems nothing to be said for this view. It has no evidence in its support.
Another version of subjectivism about sex would say that to be sex X involves having certain attitudes and dispositions. But it is quite easy to show this kind of view to be false: one simply imagines if there is something incoherent in the idea of a person of sex Y having those attitudes and dispositions. And if there is nothing incoherent about it, then the view has been falsified.
This kind of subjectivist might appeal to bundles of such attitudes and dispositions, but the same applies and plus such moves are always apt to look ad hoc.
So one doesn't need to appeal to any of the sexist motivations that lead some to endorse subjectivism about sex (and doing so is ad hominem anyway). We can just soberly assess it in the cold hard light of rational day and see that it turns out to have nothing to be said for it. (Which is, presumably, why it is the preserve mainly of the stupid and the sexist).
But still, the whole 'changing sex' issue is a red herring. FOr like I say, sex is only unchangeable if sex has an essential historical element - but it doesn't seem to. Different issues are being conflated here, then. Can one change one's sex? Well, yes. That seems metaphysically possible (and may well be practically possible too). But is sex subjective? Well, it doesn't seem to be. And thus changing one's sex requires something more than simply changing one's attitudes or thinking one has changed one's sex or some such.