I've dealt with this from time to time by positing fantasy biology rather than fantasy races.
Twelve Kingdoms is a rather extreme example of this where people don't have children per se, rather a couple who is 'engaging' regularly will feel compelled to visit a tree (call it the civilization tree since you build your villages where you find your tree) and there they will find a child waiting for them. Not frequently, but not uncommonly these children aren't human children. There all capable of being members of human society and being raised by humans, but a sapient, articulate, upright, super huge mouse - say - wouldn't be seen as anything amiss.
A solution I've used is that who you are is a mixture of who your parents were and what magical influences were active on you between conception and birth. This varies by culture. So that for some very urban kingdoms with lots of arcane energy roaming around people are heavily influence by dimensional alignments - so your kids could be Deva, Tieflings, Genasi, Dragonborn, or warforged based on shifts in the Astral Plane.
For other kingdoms with a more concrete relationship to the earth it's a question of spiritual geography. People who live near rivers become Halflings, people who live in high mountain valleys become Goliaths, and so forth. But it's variable as well. Sometimes the spirits of a river will bless the child of two dwarves and they end up with a kid who's very lean, charismatic, and hard to collar.
You could probably even break down it by caste or class as easily as kingdom. Maybe even profession - clerics spend so much time around divine energies that their children tend to be Devas or Elves.
