Ahhh...fairly typical. A question about why conservatives think what they think becomes a thread for a bunch of not very conservative people saying, for all practical purposes, they think that way because they are a bunch of jerks and losers.
Well, I'm not a conservative, either, but I think I understand the actual answer about why they say those things. I don't agree with it in many cases, and in some cases, it makes absolutely no sense, but I think that saying that some people have "special rights" is not 100% ridiculous in every case.
Basically, for many conservatives, that allegation, that some groups are getting extra rights, has become a mindless talking point, repeated blindly without comprehension by the speakers. However, its origins are at least slightly more sensible. I will try to explain the origins of the idea, and then talk about how it is often used today.
It comes from various civil rights protection laws, and the different way they affect the protected classes versus straight, white, males. Suppose your boss doesn't like you, and he fires you. Well, if you are a straight white male, you pretty much need a new job. However, if you are a member of a protected class, you might be able to sue, claiming that you were not fired for job performance reasons, but because you were black, or female, or gay. Likewise with hiring decisions. A straight white male who doesn't get a job after an interview had better line up a new interview, but a member of a protected class has a much better shot at filing a grievance with the EEOC.
Back in the days when race based hiring quotas were a real thing, it was actually the case that a certain number of jobs were set aside for black people, regardless of qualifications. That was seen as a special privilege for black people.
I don't buy into that way of thinking, but I understand it. I'm among those who think that a certain degree of protection is required simply because the evidence shows that, without them, many, many, employers would refuse to hire or refuse to promote blacks, or women, or whatever protected minorities there were. The extra protections are just a levelling mechanism. However, if a white person sees a black person get a job that the white person was seeking, he might believe that the black person got the job even though the black person was less qualified.
Those are the "special rights" that members of protected classes allegedly have. Hiring quotas are not very common at all these days, so that's not very applicable, but protected class members have the right to sue for discrimination. It is believed, by many, that this creates extra privileges for women and minorities that are not available to white men.
To my way of thinking, that doesn't seem to really work out in practice. I tend to think that even with the protections in place, there still seems to be a lot of discrimination, and white males don't exactly seem oppressed, but that's the way some people think.
Now, applying that to gay marriage doesn't make any sense at all to me. I understand some of the arguments against gay marriage, but saying it creates some sort of special rights for gay people is something I can't even wrap my head around to explain. I conclude that the speakers in those cases really don't even understand the "special rights" argument in any of the cases where it could at least conceivably be applicable. It has just become a mindless parroting. Whenever rights are extended to any other group, there are some people who simply roll out the old mantra that all legislation that protects minorities or extends rights to minorities must be granting them special rights. There's no way to explain it based on the actual meanings of the words involved, but the speakers aren't really thinking about what they are saying. They're just repeating some words that have been rendered meaningless through overuse.