This is a complicated issue that isn't easily explained. I'm not a psychologist or sociologist. However, I am a gay man of color who has endured bullying as long as I can remember in my 30+ years on this earth -- first for my race, then my sexuality, and then combination of both -- I can share my thoughts.
I think it boils down to two things: privilege and the media. And they are inherently intertwined. What follows may be a generalization/simplification, but hear me out:
White gays (in particular, gay men) are inherently privileged. Most outwardly "pass," meaning they don't disrupt the norm. People of color automatically do not "pass." And neither do transgender people, unless they fall into a very narrowly definition of the norm (i.e. feminized facial features, long hair, breasts, etc.).
Anything outside of that norm is the "other." Some might say white gay men bully because they were bullied. Perhaps. But I believe they simply bully to exert their power over the "other." In all groups, dominant types are elevated. In nature, that is the strongest. Which can explain why the ripped, jock type may prevail. But why white gays in particular?
The answer? The media. White gays are the prevailing image is gay media, advertising etc. The media in general is, but especially LGBT media? Why? There's a safeness to seeing white LGBT representations, both to white and LGBT audiences.
"Sure, they may be gay, but at least they look like me," both groups can say.
What doesn't look like the norm? A trans person of color. The "other." And because of that, white gays want to control that, to set the image of what is the norm in LGBT culture, and the easiest way to do so is demonize the "other." To portray them as so different they are not the norm. Or even less than the norm.
Before Grindr initiated their Kindr policy, I saw the most egregiously racists posts (many of which are still archived on Douchebags of Grindr). There were the blanket "No Asians" advisories, so commonplace that no one batted an eye to seeing "no fats, no fems, no Asians" on profiles. I have had guys hit me up for the sole reason of saying racist things. And if I tell a guy I'm not interested, they retaliate by saying things like "chink loser" (yes, even other Asians will say that).
And if you think words are bad, I have had horrible things done to me. Guys on Grindr have sent me fake addresses and had me drive out 30-40 minutes away to a random neighborhood, often in the dark (this has sadly happened several times). One guy gave me a fake address and once I arrived, wandered around and couldn't find the house, he wrote he hopes whoever owned the house I was at would call the police on me.
I've had a white guy literally stick his hand in my face at a club. All I did was approach him to say he was handsome, not even getting five feet near him. And I've lost count of how many times white guys have walked out on me the moment I enter the steamroom at a spa (ironically, Korean spa) or closed doors in my face.
What is the reason for their behavior? Note, in all of these cases, I did nothing inappropriate, creepy or violating towards these white guys. They wanted to establish dominance over me (and some even hurt me) on the basis of race. Because they want to have the power.
How do I know this? Because it's become so engrained that people of color are starting to act the same way. Gay Asians are super nasty to other gay Asians. I always get nasty looks from other Asians -- maybe they see me as the "other," maybe they see me as competition.
I embarrassingly find myself doing the same thing. If I see an Asian who might not speak English as well, or someone dressed very fem (as I have bought into all the media brainwashing and try to "pass" as straight as possible), I think I'm better than them and try to "other" them by staying away, thinking something mean, or even saying something.
I'm ashamed to admit that, but it's true. Sadly, I don't think a lot of white gays have that awareness of being the "other," which is only reinforced by the media. It's an ugly, difficult-to-break circle.