The immune response in the uterus is attenuated, or it would kill the embryo. as an example, your body would reject a kidney from your own child, without drugs. for that matter, you can carry any human embryo, and it won't (shouldn't) reject.
Reading on it, humans seem to rate the most receptive kind of uterus in the animal kingdom. but most research is focused on having an animal carry a human embryo, or a common / cheap species carry a rare / expensive species. The best evidence that it won't work, is no one has apparently done it yet. I suspect China is trying any crazy thing, and Russia was said to have tried all the crazy combos at one point, mostly failed. There is a wiki article that has a decent amount of information....
https://en.wikipedia.org/wiki/Interspecific_pregnancy