Calling Putin "gay" as an insult does not fight homophobia, it enforces it. I understand the impetus behind the image, and I understand the amusement that many people have about it, but as a gay man, this is just someone yelling "fag" at Putin. Images and jokes like this are homophobic and transphobic, and do not make most gay people feel safer, but more marginalized. Same thing with that huge billboard of Putin and Trump kissing outside of the RNC.
This tweet says it very pithily:
My gay, trans, and queer friends are beautiful people who are trying to live their own reality (and me my own, for that matter), but here we have the implication "LOL, this dictator hates gay people, and wants to hurt and kill them, so we're going to associate his image with queer regalia to mock him." By using queer regalia to mock someone who hates queers, you are not empowering LGBTQ folks, you are mocking them, too.
Of course, this is only my opinion, and I know lots of people want to really needle Putin with this image, I just want to maybe make you think twice. If you think of yourself as a LGBTQ ally, maybe think twice about this, otherwise those that you would like to be allied with may look twice at you, wondering if they can really trust you not to appropriate their images in a mocking way.