The Turani/Shou is literally the same of
@Mistwell 's Korean/African example. Human heritage in 5e has no mechanical representation. Any attempt to represent such a blending is 100% RP. And we're fine with that because we wouldn't DARE give human heritages any mechanical standing. It shows that we as players tolerate the concept of mixed ancestry being only aesthetic as long as there are no mechanical elements attached.
The high/Drow example shows a much better example. They are both elves and there should be no logical reason they can't interbreed. But the two types have mechanical differences. They are 75% the same traits, but the question comes on how you represent that remaining 25%.
You could have the PC pick one subtype and flavor the other in, but that's no different than the current mixing rule people are railing against. If that works for high/drow elf, it should work for human/elf. If you argue there should be a mechanical representation of that blending, I ask how. Player picks which spells/features? Do you create a "new" subtype that represents that? There are no rules for that, so you're at the mercy of what you DM allows, which can be "customized stats" to "not allowed." I don't even know if a system like Level Up is granular enough to represent a high/drow mix. And you'd think that would be easier since they literally share the majority of the same traits! But the devil is in the details.
Suffiice to say that if "pick an elf, re flavor it to half-elf/human" is bad and possibly offensive because it reduces the effect of the second parent to only aesthetics, then the Turani/Shou should be similarly bad (both parents are only aesthetics) and the high/drow elf as bad. And we let both of these corner cases ride because nobody cared until they removed half-bteed races from the game.
Which brings me to the only solutions. You either completely redesign the species system with an eye towards intermixing traits, most likely though a customization system (which, knowing most players, means pure blood species will never be used. Look at how the fixed backgrounds are already being rejected for customized ones. You really think a species mixing system isn't going to be similarly used to pick all the best traits?) or you make it purely aesthetic and just pick one set of stats.
Or I guess you decide all species and subspecies are infertile. But that seems particularly bleak, despite the fact that was the norm until just recently.