I want to refer to all couples which aren’t man-woman couples.
One expression would be “same-sex couples”. But even "same-sex" doesn't cover everything, as it reaffirms the idea of binary genders (only refers to man-man and woman-woman couples).
So, what word might I use? It should cover not only same-sex couples, but also couples where one of the people is, for example, non-binary, or gender-fluid.
A few options would be “non-normative” or “non-heterosexual” couples, as Wikipedia points out:
Non-heterosexual is used in feminist and gender studies fields as well as general academic literature to help differentiate between sexual identities chosen, prescribed and simply assumed, with varying understanding of implications of those sexual identities. The term is similar to queer, though less politically charged and more clinical; queer generally refers to being non-normative and non-heterosexual. Some view the term as being contentious and pejorative as it "labels people against the perceived norm of heterosexuality, thus reinforcing heteronormativity"
Not sure if that’s the best expression for this though, because they're a little clunky. Also, as written above, they reinforce heteronormativity.