Citation, please.

If you are worried about unvaccinated people harming others, you should be targeting male homosexuals for free HPV vaccination. But that of course would stigmatize them.

Actually, it's more that the current vaccine doesn't work as well for adults -- at least according to the CDC, but who knows, maybe they're in on it:

CDC recommends the HPV vaccine for all boys ages 11 or 12, and for males through age 21, who have not already received all three doses. The vaccine is also recommended for gay and bisexual men (or any man who has sex with men), and men with compromised immune systems (including HIV) through age 26, if they did not get fully vaccinated when they were younger. The vaccine is safe for all men through age 26, but it is most effective when given at younger ages.

Oh, so they are targeting male homosexuals. So much for that conspiracy theory.

Hmm ... it seems to me that if I wanted to invent a homophobic conspiracy theory to explain the HPV vaccination strategy, it would be like this:

"The vaccinators clearly do not want to make gay men healthier, because if they did, they'd promote the vaccine heavily for boys. As every good homophobe knows, gay men 'convert' little boys, who then grow up to be gay men. Instead, the vaccinators promote it for girls. This means they only want to help women, both lesbian and heterosexual women. Therefore, they are anti-male radical feminists."

This explains the facts at least as well as your conspiracy theory, and possibly better.

Of course, what would explain the facts even better is that medical ethics generally entail recommending a slightly-risky treatment most heavily for those who can suffer the worst from the disease; in this case, women.