Editor’s note: This story is part of an occasional Associated Press series examining the issues at stake in the presidential election between now and Election Day. Read more from “Why it matters.”

THE ISSUE

Same-sex marriage is now the law of the land, but there are other battlegrounds related to civil rights and nondiscrimination protections for lesbians, gays, bisexuals and transgender people. Two polarizing questions: What sort of access should transgender people have to public bathrooms? And are the advances for LGBT rights infringing on the religious freedom of some Americans?

WHERE THEY STAND

Hillary Clinton is a staunch supporter of LGBT rights; she has endorsed the Equality Act, a proposed federal law that would provide comprehensive protections against discrimination on the basis of sexual orientation and gender identity.

Donald Trump says he would be a better president for gays than Clinton, yet major LGBT-rights groups strongly oppose him. Among the reasons: He has balked at endorsing same-sex marriage, his evangelical advisory board has included prominent opponents of advances in LGBT rights, and running mate Mike Pence, Indiana’s governor, last year signed a law that critics said would allow businesses to deny service to gay people for religious reasons.

WHY IT MATTERS

Whoever wins the presidency can only do so much to influence national LGBT-rights policies, unless, perhaps, if the winner’s party sweeps control of Congress. The proposed Equality Act is unlikely to advance through a Republican-controlled House, even if Clinton wins. And the nationwide legality of same-sex marriage is unlikely to be threatened, though some conservatives cling to hopes that a Supreme Court reconfigured by Trump appointees might reverse the 2015 ruling extending that right to all 50 states.

On some fronts, however, the outcome of the presidential race could have a major impact – for example, in how aggressively federal agencies work to expand LGBT rights. Clinton would probably maintain or intensify the Obama administration’s efforts to bolster transgender rights. This could mean pressure on school districts to let transgender students use school bathrooms based on their gender identity.

Some transgender students have become activists on this issue, saying they face harassment and discomfort if forced to use bathrooms on the basis of the sex on their birth certificate.

There’s also the matter of judicial appointments. Thus far, federal judges have generally been unsympathetic to arguments that certain types of anti-LGBT discrimination are permissible if in accordance with a person’s religious beliefs. Trump has told conservatives he’d place a high priority on religious liberty and would seek to protect Christians from having to violate their beliefs. Among the types of cases in question: Whether wedding photographers or bakers who oppose same-sex marriage should be penalized for refusing to provide services for a same-sex wedding.

At the state level, the election could have important repercussions for LGBT issues. In North Carolina, for example, the Democratic candidate for governor, Attorney General Roy Cooper, opposes a law curtailing LGBT rights that was signed by his election opponent, incumbent Republican Gov. Pat McCrory. That law – which includes restrictions on transgender people’s bathroom access – has been the target of an expansive protest campaign.

In Indiana, Pence’s decision to forgo a second term to run for vice president boosts Democratic hopes of winning the race for governor. The Democratic candidate, former House Speaker John Gregg, has vowed to push for full LGBT civil rights if elected; at present Indiana is one of 28 states with no statewide nondiscrimination protections for gays and lesbians.

In Kentucky, there’s an intriguing U.S. Senate race matching incumbent Republican Rand Paul, who failed in his presidential bid, against Democrat Jim Gray, the openly gay mayor of Lexington. Gray is an underdog in the race.