I don't actually think this makes very much sense for the majority of Asians. The issues are complicated.

Moves for greater multiculturalism, or greater colorblindness, are one place where both groups have the same interest: you can be "othered" in a white community as long as you're non-white; it doesn't matter in which way you're non-white.

But lowering police violence is the main concern of the Black Lives Matter movement. Asians already are outliers in the opposite direction, with far fewer per-capita encounters with police of all sorts (ranging from arrests to murders). Asians have, on average, the least personal reason to care about this issue.

University admissions is another area where there is an exact tension: anti-racists who want to help traditionally disadvantaged minorities tend to argue for affirmative action policies which adjust entrance criteria in favor of, say, blacks; but universities have only a finite number of spots so there is necessarily competition, so those spots tend to come at the expense of white and Asian students. Further, if the logic for affirmative action is based on equity, then the anti-racists' position should be to raise standards yet higher for Asian students.

So, no, I don't think the groups are natural allies. They're possible but uncomfortable allies, even putting racism aside.

Or we could just say that we hope that there are many compassionate people who care about creating a just society, and some of them are black, and some Asian, and some white, and some Hispanic (some of which are one of the others too), and some none of the above or all of the above, and if we all ally in the cause of creating a just society, and figure out together what that means, we may achieve success.