Would you say the same for a female muslim doctor?
Not if she was employed by the NHS. Nor should a person who won’t touch the opposite sex be trained by UK medical schools with NHS resources. But if someone like that had completed their medical training elsewhere and wanted to set up a private practice here, why not?
We expect doctors to be willing to give emergency care to anyone in certain situations, say before paramedics have a chance to turn up and a doctor just happens to be around in an emergency situation.
So if a doctor had an absolute rule against treating men, yeah, that's a problem.
I'm not sure what the rules are if a GP in private practice just wanted to have women for patients. Maybe that's allowed.
This is quite different imo from the abortion issue. I don't think people should have to be involved in abortions; although again, if it goes wrong, and a doctor is needed for an emergency situation then that's different.