While I personally disagree with this doctor's choice, she absolutely deserves the right to make this decision. To punish her for that would be to spit on the Constitution.
Unless you've been living under a rock, it is a given that the U.S. Supreme Court, which has been greatly solicitous to the cause, will impose acceptance by judicial fiat. Because it is an extremely important issue, compared to, say, a simple thing like a federal mandate to report how many people get shot per year by cops, which black people have pursued for decades but never been able to accomplish, or the Equal Rights Amendment to enforce equal pay, which women tried very hard but failed to get passed.
Following the Supreme Court decision, expect more clamor for mandatory LGBTQ training in schools anf workplaces. The so-called suppressed minority, which now already wields an iron fist behind closed doors in Hollywood and Silicon Valley and every major city, will demand special status until there is an LGBTQ president in the White House with an LGBTQ spouse and an LGBTQ dog, and a rainbow flag in front. With penalties on the books across the land to punish thoughtcriminals for non-LGBTQ compliance. To deter unauthorized deviations from diversity in thought and action. Because there must be diversity, until there shalt be no diversity. We can't tolerate that.
The authoritarian streak runs deep and strong in the LGBTQ culture, along with a lust for revenge and a take-no-prisoners attitude, as demonstrated in this case. Beware.