Alexander wrote:

A common response is "What scientific evidence is there that scientism is itself true?". It is obvious that scientism is not the kind of belief that can be supported by the scientific method. The whole idea that "you can't believe anything without scientific evidence" soaks into people's minds as an unquestioned zinger to use against religious people, not as a reasoned point of view, and no one consistently lives by it. Honestly, I'm surprised to hear that there are any "self-proclaimed adherents of scientism". Atheism may be simply incorrect, but scientism is incoherent.

Feser has a far more detailed refutation at the opening of Scholastic Metaphysics, specifically arguing for the necessity of metaphysics to analyse the realities presupposed by the scientific method, but for the purpose of denying scientism you only need to point out that it destroys itself.

Good point. Scientism is a philosophical assumption--there is no litmus test, no distillation of a chemical agent, that objectively proclaims the primacy of the scientific method.