Rather than try to tell other minorities what they should do, I'll start with the one of which I'm a member. I don't trust gay people to decide what is homophobic, or what is antigay bigotry. Many gay people are themselves homophobic; if they can't spot it in themselves, they probably won't be able to spot it reliably in heterosexuals. And they don't.
There are two phases to the question, it seems to me. First we need to know what we're talking about when we talk about homophobia. Merriam Webster's definition is revealing:
irrational fear of, aversion to, or discrimination against homosexuality or homosexualsI've already discussed the odd conflation of "aversion" and "discrimination."
But I once had a revealing exchange about all this online. I wrote that if you are uncomfortable seeing two men kissing, but not a man and a woman kissing, that is homophobia. It didn't seem like a particularly controversial statement to me -- that discomfort is an irrational aversion, no? -- but other gay people disagreed with me vehemently. Their argument was that if you aren't throwing rocks at a gay person, you aren't homophobic. It also seemed that they were hesitant to label someone a homophobe merely for wanting to vomit at the sight of two boys kissing, because homophobes are, like, monsters -- demons, even. That's odd when you consider how much fuss there has been among my people over language like "That's so gay," which doesn't constitute overt violence either. But then, many gay people have at least claimed to be disgusted by public displays of affection between people of the same sex. They would commonly try to mask their own homophobia by claiming to be just as disgusted by heterosexual PDAs. The only disgust at PDAs I've ever observed among my fellow Homo-Americans, however, is disgust in gay men at lesbian PDAs.
I've known a fair number of people who were initially shocked (irrational aversion) or repulsed (ditto) by the idea of homosexuality, or the sight of same-sex couples kissing (or even holding hands), but who got over it -- without therapy. Their original reactions were born of ignorance and socialization, and these faded away when they got to know gay people, and their repugnance faded. Even if one wanted to call this homophobia an illness, like most illnesses it can pass without treatment. Some people, true, cling to their revulsion; that's a lifestyle choice. It can be judged morally, though a sensible person will also recognize that clinging can become a reflex that isn't turned off easily.
Many, perhaps most gay people regard as homophobic any criticism of born-gay theories of sexual orientation. Anyone who doubts that homosexuality is innate will be accused of believing that being gay is a "choice" and of siding with the bigots. This is problematic given the absence of sound scientific evidence for, or a coherent concept underlying for those theories; but as with the medical model in general, the conclusion comes first and the evidence later, if ever. And the born-gay faith is compatible with considerable internalized homophobia. (Would anyone choose a lifestyle that caused them to be hated, despised, persecuted ...?)
Having said that, I notice that "Gentiles don't get to decide what is anti-Semitic" is conspicuously absent from the meme. I suspect that many if not most American Jews would agree that any criticism of Israel is anti-Semitic, unless the critic is a Jew, in which case he or she is a self-hating Jew. Should this be allowed to stand? I know that the acquaintance who posted the meme on Facebook is critical of Israel, as am I, and would dismiss the contention and the accusation. But this can't stand, on the meme's simplistic terms.
"Non-patriots don't get to decide what is anti-American" is also absent from the list. So is "Non-Christians don't get to decide what is anti-Christian," along with "Non-Catholics don't get to decide what is anti-Catholic," and even "Non-fundamentalists don't get to decide what violates religious freedom." What complicates the problem -- and also indicates the way out of it -- is that not all members of any of these groups agree, about much of anything. There is a wide range of attitudes to homosexuality and antigay bigotry among gay people, for example; many critics of Israel are Jewish; many critics of the Vatican and the Catholic hierarchy are Catholic; feminists take a wide range of stances; and so on. It's easy, and all too common, to dismiss the dissenters as willing victims of false consciousness, but that won't work: who gets to decide who has authentic consciousness?
But too much good work on women's issues has been done by men, good work on gay issues has been done by heterosexuals, good work on race has been done by white people, and so on, to limit discussion to the simplistic level of this meme. Beyond that level, what matters is the quality of the arguments a person makes. By that standard, much of the discourse of oppression by the oppressed groups doesn't measure up, and it's not news that majorities in such groups are often hostile to the arguments made by the more thoughtful among them/us. Which doesn't mean that academics and other intellectuals should automatically have the last word either; nor can an outsider dismiss the complaints of the oppressed by pointing to one or two among them who support the oppressor. You have to acquaint yourself with the range of opinions in any group, and then think about them. That's a lot harder, but it's what has to be done if anyone's going to learn anything.