Lulz. Off the deep end of the slippery slope. But I'll respond: First, doctors take a an oath which more or less gives them a directive to treat everyon, so much of this is moot.
Woman? Depends on the type of practice the doctor runs/is part of, and which specialty/training he/she has. If it's a GP, then yes. If he's a male urology specialist, then there's no point, but owing back to the oath in cases of emergency, then still yes.
Homosexual for STD's? Yes, if that doctor is skilled in such matters. Doctors take an oath to treat the sick.
Perform an abortion? Certainly not if the doctor is not trained in such procedure. But if a doctor does get trained of his/her own volition, then it's probably safe to assume they'd be comfortable in performing one.
Also, there's well-established case law that establishes that doctors really cannot discriminate at all:
"...physicians are only free to refuse to accept a prospective patient if their reason for doing so is not prohibited by contract (e.g., with their employer or an insurance company) or by law. And there are several laws at the state and federal level that prohibit certain types of discrimination in the context of offering public accommodations – including discrimination against patients."
http://blogs.harvard.edu/billofhealth/2012/09/07/discrimination-in-the-doctor-patient-relationship/