If you look at the hashtag, it calls it "femmephobia". This is actually consistent with similar posts I've seen, like one where a girl said that having tattoos and a "butch" haircut didn't make her gay or trans, and people called her out for homophobia and transphobia. The reasoning is that, if you feel the need to fight stereotypes, then you view those qualities as "problematic" or "negative" or "bad"; why else would you feel the need to correct people if you were afraid of being associated with those traits? This means it's becoming more difficult to fight stereotypes, because being mistaken for gay or trans shouldn't be some horrible mistake to fight against, which is what you're doing in their eyes. By pointing out that he's not a stereotypical gay man, the responder probably saw it as a proclamation that these traits are inherently bad for gay men to have.
The way I'm seeing it is that it creates the issue of "fighting stereotypes to destroy gender roles that are the root cause of some of our social problems" vs. "letting marginalized groups uphold those same stereotypes so they that have something claim and take pride in".
