Every person has mixed ancestry at some points in their history, but one of the main products of the melting pot is people who are recently mixed, people who can identify their recent composite races.
It's been the normal custom throughout history for males to 'be' the race of their fathers and females to 'be' the race of their mothers, but melting pots often are also a mix of politics, and people commonly confuse their origins to adapt to some political expediency.
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At some point in the future, there might be three perceived races among most people.
1) The original race of humans which diverged into many races.
The common paradigm, and that which the current popular scientific mind sees as 'obvious', is that there were numerous 'original races' which dispersed over the globe and formed the various groups existent today. Of course the 'original' races had to have a common root, and that common root descended from 'original races', ad infinitum.
"Nuclear and mitochondrial DNA are thought to be of separate evolutionary origin, with the mtDNA being derived from the circular genomes of the bacteria that were engulfed by the early ancestors of today's eukaryotic cells."
https://en.m.wikipedia.org/wiki/Mitochondrial_DNA
A more historically useful paradigm is that there was one original race, a pre or early human group, from which all modern humans diffuse / originate. This would be a geographically spread out group of human ancestors, analogous to how today’s various races have roots in different areas. The analogy will be complete if humans keep expanding and any currently isolated groups are able to speciate.
example / some unknown early hominid species from which almost 100% of modern human DNA originated.
2) The male and female races.
There is a possibility that men and women are more 'two symbiotic species' than 'two halves of one species'. Very speculative but possible. It's a paradigm that appeals to some, not to others, but it could develop as mainstream. It’s based on the obvious roots of the two genders in two different symbiotic organisms which combined to form the precursors of animals. See above Wiki quote on mtDNA.
https://en.m.wikipedia.org/wiki/Evolution_of_sexual_reproduction
https://theconversation.com/the-y-chromosome-is-disappearing-so-what-will-happen-to-men-90125
https://crev.info/2018/02/y-chromosome-disappearing/
3) The local race.
If parts of the various human tribes that are still fairly distinct races can continue to evolve apart from melting pots 'post space travel era', then there will be a rapidly growing diversity of ethnic races. Space colonization might allow this but any isolated group that has even a small amount of outside DNA would probably not evolve as fast in a unique direction.
In the past there was not space for two hominid races in one region, there still is not today, but space travel may change that in a hundred years or less.
If that does occur and numerous isolated human populations survive, there will be all sorts of Darwinian adaptations to space that will cause human groups to diverge much faster than they have on earth,
At some point the divergence will be fast enough that where a person is in outer space will determine what the local race is. Since a background of 'too much genetic diversity' is as fatal to a species as a background of 'not enough genetic diversity' is to an individual, there will probably be attempts to limit sub groups of humans to regions of outer space.
It's considered a 'racist theme' to even examine the negatives of increasing racial diversity, but at some point the political correctness will have to yield to facts.
https://en.m.wikipedia.org/wiki/Genetic_diversity
https://en.m.wikipedia.org/wiki/Outbreeding_depression
https://en.m.wikipedia.org/wiki/Heterosis
Horses were well adapted to many environments, and spread around the world, presumably with access to genetic diversity in the long term from distant subgroups. In other words there might be a several hundred year delay, but the genes of a horse in one part of the world would have reached a separate population in another part of the world.
Horses went extinct in North America about 7,000 to 10,000 years ago. Some people speculate their extinction was due to humans but that seems unlikely. There have probably been many other species as well that expanded and then both consolidated in a region and continued to diversify with distant groups that were consolidating. If it were a good genetic strategy there would be a lot of evidence for that, but the lack of many such species, and the general tendency of species to succeed long term as one isolated population, seems significant even if it isn't easily explained in an inoffensive way.
https://en.m.wikipedia.org/wiki/Horse
It seems likely, from nature, that a species goes through phases. When it has just differentiated and is expanding then genetic diversity is good. Once it has reached a 'consolidation' phase then there is probably a price for continuing to diversify with other sub groups. Whether the human race, or any specific sub group, benefits or loses from being 'melting potted' will probably become clearer in the future, but the fact that there are many species, rather than few, would seem to point to their being some mechanism that prevents any one species from continuing to both consolidate and diversify in any ecosystem.
~In Progress
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Many traditions have ancestor legends about an early race. There is a blurry line between whether these legends refer to a past or a future.
https://en.wikipedia.org/wiki/Epic_of_Gilgamesh
http://www.ancient-literature.com/other_gilgamesh.html
http://looklex.com/e.o/texts/religion/gilgamesh01.htm