Strange Sauna Rules about Nudity?

OK I have had a very strange experience in the sauna here, and I am wondering if this is normal in Switzerland:

Long story short, I went to the sauna with my wife today. OK I will say it's strange to me that they mix men and women in nude saunas, but I thought "ok it's not your culture, probably they find it normal". We go in, and there's three men laying spread-eagle leaving nothing to the imagination. I've been in plenty saunas like this before, but never in a mixed sauna. But okay whatever, still just thinking "live and let live" at this point.

So I had a towel around, and my wife had on a swimsuit. Then this old guy sits up with his legs spread, and tells my wife that she needs to take off her swimsuit. I was like "excuse me?!" Then one of the others joins in and the two of them tell her to take her swimsuit off. I told them to politely mind their own business, but that was already waaaay over the top in my opinion.

Whatever. Wife and I lay down and try to relax.

Then, one of them goes out into the lobby to get a worker at the sauna, who then comes in and DEMANDS that my wife REMOVE HER SWIMSUIT. I'm like wtf are you people talking about? The worker says "that's the rules" and I told her I don't believe her, because how on earth is it your business what my wife is wearing in the sauna?!

Eventually she says "if you don't follow the rules you have to leave". I am fully taken aback at this point. We just go into the (separated by men and women) changing rooms, pack our stuff and leave.

My question is this: What the hell is this? Is this normal here? How? Why? I have so many questions. . .