Insofar as “Asian” is considered “not white”, it would seem that it would be counter to an asian person’s self interest to advocate for white supremacy.
Of course, whether light-skinned Asians are considered “white” is a question of an arbitrary social convention which differs not only between groups of people, but also the contexts in which the question is considered. (The concept of “white people” is a mistake, which ideally will be made obsolete.)
Also, even if it was clearly against their self interest and they knew it, that wouldn’t strictly speaking logically preclude it.
But, if people expect that advocating for white supremacist stuff is usually motivated by something like self-interest, one generally expects it to be, for the most part, (excepting the rare exceptional individuals who have rather unusual motivations) to be people who would be considered “white”.
(Though, if someone is “white passing”, in the sense that people might initially consider them to be “white” if judging only by appearance, but might change one’s mind if informed of their ancestry, then such a person might have less incentive to avoid white supremacist stuff than someone who very few people would ever consider “white”.)
Does this answer your question?