Japanese Wikipedia literally translates this noun as 平等【びょうどう】結婚 (source), and some Japanese sites introduces 結婚の平等, 婚姻の平等, etc.
I think all of these are valid possibilities you can use, while 結婚の平等 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 同性婚 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 同性婚 or 同性間の結婚.
結婚が各性的指向に認められました doesn't make sense to me.