2:05 PM PT -- Yep, no way this controversy's going away ... 'cause Republican VP candidate J.D. Vance just mentioned it during his rally in Georgia -- claiming the far left thinks it's okay for men to punch women in the face.

Imane Khelif's dealt with a very emotional week ... with tons of people online questioning her gender and calling her names -- and, she let it all out after her quarterfinal win.

The Algerian Olympian beat Hungary's Anna Luca Hamori Saturday morning ... winning by a unanimous decision in her QF match -- and, tears immediately came pouring down her face.

Watch the video, Imane leaves the ring and her team has to comfort her -- with racking sobs coursing through her. It ain't just about the punishment in the ring obviously ... it's about all the pressure outside of it too.

Of course ... it's been widely reported Khelif has XY chromosomes -- but she's still biologically female and allowed to compete according to the International Olympic Committee.

However, she's thrown some ferocious punches in the tournament so far ... and, Italy's Angela Carini withdrew from competition after less than one minute of fighting Imane.

The withdrawal pushed many celebs -- among them Logan and Jake Paul, J.K. Rowling, Elon Musk and more -- to bash the 2024 Olympics for allowing a man to fight a woman. Again, Khelif is a woman, not a trans man, as many have claimed.

Carini has since apologized for refusing to shake Khelif's hand ... but Hamori apparently posted multiple photos to Instagram this week attacking Imane, including one implying she's some sort of beast.

Now, Khelif's on to the semifinal match ... but, we don't think the controversy's over yet.