Except in the case of massive social upheaval, I think co-ed showers will never be the standard. As @Samuel said jokingly in a comment:
Probably when men stop excitedly asking.
This is quite a humorous comment, but there's a much more serious way to put it - separate bathrooms and showers will always be around as long as rape is still a thing. One rape is all it can take to bring a costly lawsuit down on the heads of whatever organization owns the building.
The only place for co-ed showers is one in which everyone using them feels safe. It's hard to imagine a society in which every single woman feels comfortable having men be able to see them naked without the woman being able to do much about it. Men can also be victims in situations like this - there are male victims of rape.
Co-ed showers can be put in place in limited locations, such as the "clubs and venues which target alternative lifestyles" that @HenryTaylor mentioned. The people that go there expect it, and choose to use them because they still feel safe there.
I wouldn't be surprised if society moves in the opposite direction that you're thinking - rather than having a single co-ed shower, we'll have more single-occupancy showers. It doesn't make as much sense from an efficiency standpoint, but what is there about legal issues that would make you think efficiency is anywhere on their minds? Also think about this question - how can the mother of a 6 year-old girl tell the difference between an honest transgendered person and a committed pedophile man? The best way for a facility to protect itself from lawsuits from both the mother protecting her child and a transgendered person wanting to use the bathroom they think is the right one for them would be to have single-occupancy and family bathrooms.
Even space constraints alone won't bring about co-ed showers - if you have enough room for two showers, there's no reason you can't have a divider between them that turns it into two bathrooms. So you've either got a single-occupancy bathroom, or enough room for more than one.
A dystopian government, like the one @MrDracoSpirit mentioned, might impose co-ed showers on certain groups of undesirables, but I would not count that as becoming a standard. That government would need to keep enough people happy to prevent a complete revolt, and those people would not be forced into co-ed showers. So rather than becoming a standard, co-ed showers would be seen as a sort of punishment.
@MrDracoSpirit's third point is something that would definitely make co-ed showers likely. If culture lost interest in sex, then rape would most likely stop being a thing. And that, as I said earlier, is something that would make co-ed showers reasonable.