Eric Muller (IsThatLegal?) points out that some people may indeed be “self-hating Xs”: “[B]ecause the person’s X-ness is very important to him or her yet also at some subconscious level causes or has caused him or her a great deal of discomfort, he or she denies and even flees from his or her X-ness[, and m]aybe even disapproves of or is somehow repulsed by visible X-ness in others.”
Doubtless this is so for some people, and if you really know a person well enough — preferably from personal acquaintance, but possibly from serious observation of his public comments — you might be able to legitimately criticize the person as “self-hating.” But my point, which I stand by, was that many people use the “self-hating X” locution without any real evidence of actual self-hatred.
Rather, the term tends to function (not always, but very often) as a cheap smear, or at best as an entirely unsupported inference that any X (Jew, homosexual, Asians) who might find flaws in common attributes of fellow Xs must surely exhibit the psychological profile that Eric describes. So if you do have evidence that someone really is self-hating, that’s fine. But in my experience, very few uses of this term actually rest on such evidence.