Why do you believe there are precise criteria by which "white supremacists" can be definitively identified? Some are more blatant than others, some more furtive, some tacitly share agenda and prejudices, and some naïvely swallow paranoid conspiracy hoaxes such as
"replacement" nonsense.
The vital thing is that
white supremacism be unambiguously rejected and condemned by anyone in a position of power who is associated (even if they are in denial) with it.
When Representative Cheney, who had been in the House GOP leadership, states,
"The House GOP leadership has enabled white nationalism, white supremacy, and anti-semitism. History has taught us that what begins with words ends in far worse. @GOP leaders must renounce and reject these views and those who hold them."
where is the harm in the House GOP leadership doing just that?
Why wouldn't they?