The problem you describe only concerns people who don't know anything about the subject, but still have no shame to have strong opinions about it.
Nobody in race sciences (anthropology, etc) claim that there are only unique races that are separate from each other and don't mix. This is a clear strawman.
The fact that there is mixing between races does not mean that races don't exist. You can make an emulsion out of water and oil, but water and oil still are their own things.
And the science has all kinds of specific categorization for human groups that go way beyond the rough separation into 3-4 main races. All the mixing, separation, migration, isolation, etc have been taken into account.
It's a pity this kind of topic/science is basically a taboo in the Western World and for real info and honest discussion have to go to other systems/countries/languages.