Gender and Sexual Minority, LGBTQ+, and queer all describe a largely similar set of folks.
Queer arose not from "woke-leftist" spaces, but grew out of 70s and 80s radical gay and trans spaces - groups like the Gay Liberation Front - who were willing to fight back (violently if necessary) against violence and discrimination.
Queer is absolutely a political identity, a framing of ones gender or sexual identity. They intersect with one another. It's not unlike "I eat only plants" vs "I'm vegan", they mean roughly the same thing until you hit contexts where they don't.