You can turn any political belief into "someone's rights". There are people who believe abortion is a woman's right, and others that believe legal abortion is an unprecedented holocaust. I believe we should be able to work together and respect each other while we work that out.
This is enforcing an ideological litmus test on the industry, policing people's internal beliefs. It is terrifying.
Sure, the world is not black and white, you can always twist things around and mince words to support any viewpoint. But you picked a bad example, because the argument with abortion is that the unborn baby has rights too.
The only way you can say gay marriage violates someone's rights is to say that people have the right to not be offended, or the right to hate people who are different from them. For all the contortions that people will make on this issue, it's fundamentally about fear and hate and nothing more. Abortion is a much more nuanced issue.
This is enforcing an ideological litmus test on the industry, policing people's internal beliefs. It is terrifying.