Not related to marriage rights but it’s pretty obvious that trans rights is the next big issue that’s being pushed nowadays. There was also that whole forcing businesses to make cakes for gay weddings thing (don’t remember the details but it was a whole controversy about rights of businesses to refuse service vs constraints due to discrimination laws).

There is a movement for polyamorous marriage. A city in Massachusetts just recognized that arrangement for domestic partnerships. I think, like with same-sex marriage, most people would struggle to think of a reason to be against it that isn't rooted in appeals to tradition.

https://www.lgbtqnation.com/2020/07/massachusetts-city-begin...

For animals, there's the Harkness Test.

Note that the dissent in Obergefell (the case ruling that states had to recognize gay marriage) actually explicitly said "It is striking how much of the majority’s reasoning would apply with equal force to the claim of a fundamental right to plural marriage."

No, they're pushing for free trans surgeries and puberty blockers for kids instead.

It doesn't literally have to be the exact same issue over and over.