The ROCOR parishes I've attended don't separate, but a lot of women stand on the right hand side.
My parish (Greek) has the left side as women only and the yiayiades will eat men who dare to stand there

But the other side is mixed and there's a lot of women over there, even older ones (although not the tiny all in black yiayiades who are 90zillion years old) especially those who want to sit with their families. When I'm on my own I sit on the left, out of habit, when I bring my family I sit with them on the right.
At the weeknight liturgies, which are mostly attended by youth, the gender separation is more obvious, weirdly. Noone's ever said anything about it, it's just what we do, although at the back of the church sometimes you get couples sitting together on either side.
Oh, and the Antiochian parish that was 'home' for a year and a half when I first became Orthodox, I've stood/sat on the right hand side from day one. Mostly because that's where the chanter's stand is, and I sit in the first row back from it for the same reason - this way my catechist (who brought me to Church in the first place) could pass me translations or tell me to chant or read things from where I was standing. Often it was just the two or three of us for matins or a weeknight service during Great Lent, so even as a catechumen I was in the choir out of necessity. When I go back there (the service is much later in the morning, so it's easier for me when I'm well enough to go but not well enough to leave the house by 8am) I go to exactly the same place as always and people are always happy to see me even though I'm only there once or twice a year - and they STILL rope me into the choir. Do not ask me about getting told to chant the Resurrectional Troparia when I haven't chanted anything in Church in about a year let alone an Arabic melody that I only half remember...