But you believe that most kids who deviate from standard gender roles are gay? If not, there's no reason to believe that gays would be overrepresented in abuse statistics if this deviation was the cause of the abuse.
Right. So if gays aren't more likely to deviate from standard gender roles, there's no reason to think that they would be more likely to be abused, if deviation from gender roles is what leads to abuse.
Peer abuse is rampant, so it's almost inevitable that any given gay person will have been abused. The abuse that comes from being perceived as gay based on stereotypes tends to be more violent and persistent.
You didn't provide the studies you base your opinion on, so I have no way to know if your claim that the two have been linked is true.
Again, if gay people are not more likely to act in a stereotypically gay manner, and you've said that they're not, then there is no reason to believe that gays are more likely than their straight peers to be abused for behaving in ways that are perceived as gay.