It's immune in the sense that there is no logical "criticism" of homosexuality (that is, the sexual attraction to a person of the same gender) because it is simply a fact. The question above is like asking if you are immune to criticism over the fact that you are a certain height or hair color. A homosexual person is not immune to criticism for an unrelated matter, but to criticize homosexuality itself is pointless and illogical.
I mean, it's a stretch to say that anything in this life is immune to anything. But, are the reasons homosexuality is criticized actually warranted? My answer: No.
Now one can perhaps critique the social expectations and behaviors that result from homosexuality, just as one can do the same for heterosexuality. For years, within heterosexual associations, a societal mindset has been developed that men are the go getters when it comes to sex, and women are the prize who are otherwise shamed if they partake in the same promiscuous behaviors as men. That idea has much to be criticized, but it's not because of heterosexuality by itself, it's because of people and the gender roles they decide to construct for themselves. If something similar to that happens for homosexuality (which it probably already does), then yes, it should be criticized.
But at this point, I don't think people are thinking that deeply into homosexuality and rather are just criticizing the sexuality for the sexuality by itself. And that's the part that is nonsensical and shouldn't be considered justifiable.
Sounds like homosexuality is so whiny and weak that it needs an unjust advantage just to stay in the game. Do Christians claim special protection from critics or do they predict the criticism as vindication? What doesn't kill you make you stronger...Not sure if that's true but homosexuality is too afraid to find out.
Just because you are different doesn't mean that you are immune to other people's disagreement. If you want to criticize the fact that some people have sex with others of their sex, than fine, go for it. I have a friend who once remarked that heterosexuals are just plain boring, simply because (at least, as far as I could tell) they were the status quo, nothing more, and nothing less.