The Homosexuality Cartoon says that because they aren't born that way, gays should not be eligible for civil rights protection. Christians and Democrats aren't born that way, yet under federal law, they receive protection against discrimination. Whether or not the gays are born that way is irrelevant to the discussion of trying to decide if they should be afforded protection.
As far as the twists and turns of logic that these cartoons make, I think my favorite is: We know gays are not born that way because in the late 1970's no one made the claim that gays were born that way so their claiming that they are born that way now is nothing but public relations puffery. [I need to sit down because I am so dizzy from following that]
I also want to note the subtle accustation of child molesting: "whether you are a homosexual or have just been suckered into a few homosexual acts by some predator..." [all emphasis in original text]