As others have said, it really depends on the horses, but unfortunately you can’t always predict in advance. Their personalities can totally change once the mare is introduced and changes the herd dynamics.
Various combinations I’ve had:
2 mares 1 gelding - totally peaceful, no problems
1 mare 2 geldings, all were completely asexual and I could take any of the three out of the field without drama. Then I added a 4th gelding to the herd, a mellow QH retiree that I knew very well (which is why I agreed to take him). The new QH had been in an all-gelding herd for a number of years, and this newfound proximity to a mare just blew.his.mind. Screaming, running the fence, all day long.
Even worse, the resident lead gelding, a 22yo who used to completely ignore the mare, now decided he needed to try his hand at live cover-- and the mare decided she was in perpetual heat. It was such a nightmare! No fencing or turnout arrangement worked to reduce the drama, and the new guy lost so much weight in just a few weeks that I had to send him back. Felt bad but someone --human or horse–was going to get hurt.
I’ve had my mare out with two geldings before and most recently have done both my mares with one gelding. Never had a real issue with either scenario. The only “problem” I’ve had is every gelding I’ve had my red mare out with they’ve fallen in love with her LOL.
My gelding lives with four mares. He could care less but one of the mares is very attached to him. She carries on like she’s all alone if he’s not out in the pasture with her.
Another mixed herd issues person. I do know of friends with individual horses that had domineering or anxious tendencies, and had to be more carefully managed.
However, the barn owners who seem to be most insistent on sex separation were also keeping horses in small areas and not being smart about feeding.
In one case, the woman was one of those two flakes per horse hay-rationing types and if the horses needed calories they got exotic blends of grain. So what ended up happening was violent competition for hay during turnout, and additional battle royale at the gate to come in because they were so hungry and probably ulcery, too.
My horse doesn’t have any issues with other geldings. No study behavior/ fighting, etc. I didn’t do his gelding and I haven’t tried a hormone test, so I’m not 100% sure. The only behavior is during mixed herd turnout, so my simple solution is no mixed turnout for him! 
What bothered me most was her outright deception and irresponsibility. She was an instructor, an employee. She didn’t tell the BO. She expected everyone to treat her horse as a gelding because she didn’t want him to live alone – like a stallion does.
I have one mini gelding that has lived with between 2-4 mares at a time and done fine with all of them. He does get a bit crazy when some of them are in heat but everyone is still easy to handle. I ignore any hollering when some are out being worked.
I’ve never had problems with mixed herds. Most recently I had two geldings and a mare. They had been together just the three of them for about 7 years. When I brought in another mare, the geldings were fine but the original mare was a terror. I was never able to figure out if her problem was that there was a new horse, or that the new horse was a mare. That was also the first time I’ve ever had problems introducing a new horse to a herd. This new herd was together for a little under a year before the original mare left, and there was tension in the herd until she left. So I agree that it depends on the horses.
I am of the “wont know until you try” camp of mixed turnout. I have seen (and owned one) geldings that herd and “breed” mares and many more that fight over the mares when they were peaceful before. And I have seen geldings that dont care about the mares at all (frustrating them when they are in estrous). Amazingly, one of the “dont care” geldings was a former breeding stallion with progeny.
Current barn had paddock turnout and only one mare. She goes out with one “boyfriend”. Putting her in a larger paddock with three geldings resulted in a falling out between the boys.
