If souls have races what kind of race is a mixed persons soul?
Probably mixed.
Souls having race sounds weird, until you realize souls also have sex, personality, talents, traumas, habits, preferences, karmic patterns, etc.
When you look at it like this, souls also maintaining something as fundamental as race is a no brainer.
The proper way to analyze this is not starting from the soul, as we don't fully understand the soul. We start from reincarnation, which we more easily can rationally understand.
A soul, when reincarnating, needs the proper vessel. That means the right family according to the soul's karmic patterns, the right genetics for certain talents to manifest, the right life course for certain karmic patterns to happen, and of course, the right race.
Can a white person reincarnate into a black body? No, it wouldn't end up creating the same person that died, you'd be someone else entirely.
Same with a black soul in a white body, etc., pretty self explanatory.
What about mixed races?
Well, souls don't have race "materially". Souls don't have melanin, an eye color, or whatever, in the same exact way bodies do.
What souls do have is a script of sorts, which records all things (and their karmic consequences) that made you, you. If we remove any of them, you're not you anymore.
In that sense, we can look at how race functions materially, and determine certain parallels.
If someone is mixed, they show bodily genetic characteristics from two or more races. In that case, to fully reincarnate without any issue, all of that needs to be preserved, thus needing a mixed body with the same exact admixture.
However, that's easier said than done. Pure races means easier reincarnation.
If the soul can't get a perfectly accurate vessel in time before it dissipates, what my guess is is that the Gods "force" certain things to fit together.
No two white-black mulattos are mixed in the same exact way, so I assume this forcing has to happen very often.
The soul will probably adapt, but there will be incongruence, which will likely result in traumas and issues.
Some cases are even more complex. White traits are recessive, whereas Black traits are usually dominant. So a mixed person can more easily incarnate into a pure Black body, but never into a pure White one, as the White traits are easier to lose and harder to get back.
This is the main metaphysical reason that race mixing is dangerous, besides material reasons like destruction of generations upon generations of living culture.
In short, the question is hard to answer, because the metaphysical racial structure of the soul is designed to work with pure souls in mind. Mixed souls muddy the waters, and make explaining these things complicated, as there are still gaps in what we know.