While it would be foolish in my opinion to outright dismiss a shiduch over race, after the third date or so if it is something that really bothers you (i.e. you want purebred genetic ashkenaz children or whatever) than I think its a valid issue. People want all sorts of superficial things in their spouse- racial and ethnic background is no different than many of the other superficial things people want.
I know all of this is common sense but it doesn’t hurt to repeat it.