Yes, after an ecclesiastical divorce which a hierarch may grant or deny in the exercise of economia or akrivia. We allow 3 marriages no matter how they end, but no more, even for emperors, kings or other sorts of aristocrats and elites. A first betrothal and marriage service is joyous, a second toned down and business-like and the third positively funereal.
People who live together without being married in The Church may not receive communion, whether it is a straight or gay couple. They may not act as “sponsors’ (best man/woman, godparent)If they present themselves, they are refused by the priest which can cause some commotion as I am sure you can imagine.
More than 1000 years ago, Rome allowed this too, but allowed so many remarriages that it became a scandal and the Eastern Patriarchs ruled there could be no more than three marriages.
And polygamy and same sex marriage are not now nor have they ever been a problem in The Church in the East.
When did Christ allow three marriages, now matter how they end?
Talk about “nonsense”! Look at at your own religion.