The singer posted a photo of her and Dylan -- who's transgender -- and made a point to slam trolls who reacted to Dylan's own IG post from Friday (International Women's Day) that featured her and Gaga together ... which got a massive amount of hate in her comments.

Gaga writes, "It’s appalling to me that a post about National Women’s Day by Dylan Mulvaney and me would be met with such vitriol and hatred. When I see a newspaper reporting on hatred but calling it 'backlash' I feel it is important to clarify that hatred is hatred, and this kind of hatred is violence."

She continued, "'Backlash' would imply that people who love or respect Dylan and me didn’t like something we did. This is not backlash. This is hatred."

LG adds, "But it is not surprising given the immense work that it’s obvious we still have to do as a society to make room for transgender lives to be cherished and upheld by all of us." Gaga says she's protective of the trans community ... but says she doesn't speak for them.

Gaga finishes by saying ... "I hope all women will come together to honor us ALL for International Women’s Day, and may we do that always until THE DAY that all women are celebrated equally. That all people are celebrated equally. A day where people of all gender identities are celebrated on whichever holiday speaks to them. Because people of all gender identities and races deserve peace and dignity."

In other words ... Gaga is fully in Dylan's corner here -- and says people oughta back off.

Dylan, of course, is no stranger to controversy. Remember ... Dylan faced some serious outrage online over her partnership with Bud Light last year -- which sparked a massive boycott, and hurt Anheuser-Busch's bottom line.

Those who opposed the collab, including Kid Rock, vowed to purposely not buy the beer brand -- even going as far as to destroy cans they'd already purchased. ICYMI ... Kid Rock even went viral for shooting up cases of Bud Light over the partnership.

The response wasn't all negative, though ... Paris Hilton, 'Drag Race's Sasha Colby and more voiced their support for Dylan in the aftermath.

Dylan now has a new champion in Lady Gaga -- who is a pretty powerful ally, FWIW.