The situations are quite different, and it is natural law that reveals the difference to us. Natural law is a sense of good and evil that is written on the heart of every person. It tells us which acts are good and rational and which are evil and irrational. Natural law tells us that not every kind of behavior is a right. The act of murder is not a right, nor is incest. These go against human nature. We inherently know that these are wrong.
If, for example, many people began telling us that incest is a right and that to deny such a right is similar to discrimination because of race or sex, our first reaction would be moral outrage. For a parent and child to have sexual relations with one another violates the very nature of who they are in relation to one another. Something is out of sync.
But eventually we might be swayed by such argumentation because of the sheer volume and intensity of the propaganda, not because of the rationality of the argument. This is what has happened with the so-called right to homosexual "marriage."
For two members of the same sex to have genital relations violates the nature of who they are in relation to one another. Their bodies are simply not designed for it. Something is out of sync.
The problem is that in our culture we tend to put feelings before right reason. Reason would tell us that in such a situation, one ought to put feelings second. For rational creatures to make reason subject to feelings is to court disaster.