Chances are if an Asian man is fourth, third, or even second generation, this issue may not prove prohibitive in the least.
This, much like the previous example, is not then specific to Asian men but rather an issue which could stem from being an immigrant from another country/having parents who are immigrants.
There are of course exceptions I am sure but I would argue that no matter what, men have never been held to the same standard as women in regards to maintaining cultural/racial “purity” and may as a result have more power to decide whom they date and/or marry than a non-Asian dater may initially think.
What is more, even if this concern were entirely true, its degree of significance would largely depend on how long the family in question had resided in the United States.
For instance, as a whole Asians are seen as small, quiet, and unassertive (which in a Western context are coded as feminine), whereas Black people are presented as big, loud, and physically dominant/imposing (which in turn are coded as masculine).
Before I get to the heart of my response, perhaps I should preface it with a little information about myself.
I am a 32 year old Korean American man who was adopted from South Korea when I was nine months old.
Thus while one could potentially make a case for a relationship between a Black man and an Asian woman (the ostensibly most masculine with the ostensibly most feminine), a potential relationship between an Asian man and Black woman may seem laughable if not inconceivable.
However, upon further interrogation we see how such an assessment is not just problematic, but entirely fallacious.