"It matter that we treat gender critical beliefs like any belief system because in doing so we show how hollow it actually is."

Careful here. "Belief" doesn't necessarily mean "untrue." It merely means that it can't be demonstrated empirically. That's really a relative criticism, too, because empiricism itself has only relative value. It has long been my position that, for example, my seeing myself as a woman is my belief, while a gender critical person's seeing me as a man is also a belief. What's important is that each of us be free to pursue our respective visions unmolested.

"It then begs how do you counteract such an entrenched belief system."

This is really a political question, and, as such, is secondary -- if it is relevant at all, which is at least open to question. Our best response to hostility of this nature is to simply stand: to live our truth without apology and without asking permission, and let the chips fall where they may. This may seem like a risky strategy; but, in the end, it's the only strategy; political agitation is, in the end, always about asking permission.