If the donor is donating anonymously, they do not know who is receiving the eggs. For instance, I have worked with a family that needed donor eggs. The donor is unaware of my IPs genetic makeup. The resulting children are of mixed race. The IP in this case did not choose to undergo genetic testing because there were no risk factors(known genetic risks, age, etc).
Now in surrogacy there are processes like you mention however they are more on a compatibility level between surrogate and IP as well as a mental stability level of surrogate(counseling and mmpi/psychological exam). Also there are STD, drug and tobacco, and health and background checks run on the surrogate. And then when regarding funding, escrow accounts are usually fully or partially funded to protect the surrogate. Sometimes there are home checks.
As far as gatekeepers, there are checks and balances along the way. You have REs, you have counselors, you have attorneys, you have background checks, you have PBO, court proceedings, post birth orders, etc. The specifics will depend on your state. But typically, surrogacy does not discriminate based on sex, religion, sexual orientation, or marital status.