Japanese Wikipedia literally translates this noun as (source), and some Japanese sites introduces , , etc.
I think all of these are valid possibilities you can use, while seems to be the most prevailing, according to Google. But whichever you choose, you have to explain what it means first, because vast majority of Japanese speakers don't know these phrases. I personally haven't seen any claim that is a biased term. This situation may change within a few years, though.
I checked several Japanese sites which contains these keywords, including sites which actively support LGBT. Many of them just briefly introduce these terms using brackets as (literal) translations of "marriage equality", and then stick to or .
doesn't make sense to me.