I don't think the blood type matters much in a first time normal healthy pregnancy. Neanderthals were rh negative so naturally they would want an rh- surrogate for the baby (rh- blood is found in populations with higher neanderthal genes and some believe it originated with them).
I believe the blood type often isn't a problem until delivery which is why an rh- mother can often give birth to an rh+ baby ONCE often with no problems, but without drugs to prevent rejection her body will reject any future rh+ embryos.
There is even some controversy about using pigs as surrogates for human offspring, apparently it sounds quite feasible (presumably instead of outsourcing to India which is what many folks do now). It is a pretty astounding article:
http://www.asutriplehelix.org/from_bacon_to_human_babies