The pre-collapse Soviet countries were more left and more militaristic than any others. Homosexuality was punishable by prison in the Soviet union and Cuba (ah, Cuba until the 80s, says Wiki).

As for sexism, women in Red China or the Soviet empire were more equal in their education and careers, but also got raped a lot more in the gulags.

Militarism and homophobia (outside the United States) do not correlate much at all with left/right ideology.