That's a meme that I guess is supposed to be conservative, even if it is liberal. I saw it earlier on a T-shirt opposing gay marriage.
OK, I have written countless posts taking issue with the idea of gay marriage. There are many arguments which can be made against it, but the above is not one of them.
Anyone who thinks a moral wrong is not a civil right should reread the First Amendment, and the Constitution.
Burning a Koran or opening a mosque at Ground Zero also may be moral wrongs, but they are certainly also civil rights.