In many European countries, it's not at all controversial to have nude mixed-gender saunas (and concerns about homosexuals recede once it's possible to be ogled heterosexually in such spaces).
You need to understand that straight women don't fear gay women the way straight men fear gay men. Additionally, concerns might recede for men, but I wouldn't think for women. Straight men ogle them more than gay women ogle them. Very different situation.
This is highly cultural. And I'd be surprised if, in the US, men "fear" gay men the way you're making out. But as OP clearly stated, there are countries where mixed sex naked saunas/spas are a thing and ogling or other kinds of harassment are not a big issue.
Ogling for women carries with it the implied risk of rape due to natural differences in physical strength, and women experience rape at a much greater rate than men, so that threat would have higher salience than any equivalent gender-based insecurity.
Not everybody is comfortable being naked in front of others generally, and that's okay, but straight men who genuinely fear the possibility of simply being visible to gay men need therapy. The assumption that everybody is just going to be ogling everyone else just doesn't hold up to reality where there's a very long history of people being naked in locker rooms, showers, bath houses, beaches, saunas, etc. while still being polite and respectful of each other. That isn't to say that rude people have never existed, but that is far from the norm and nothing to be fearful of.
I guess it depends on what you mean by "pursue". If a person knows that somebody is not attracted to their sex and that person still asks them out or hits on them that's just plain rude. I 100% agree that's wrong. Nobody likes that.
Asking out someone before you know how they feel about you (and the rest of your sex) is perfectly normal and sometimes that's going to result in a gay man asking out a straight man and that's okay too as long as that person backs off after getting a polite decline. I personally think it'd still be weird/rude to do that to a stranger while one or both of you are naked, but it probably does happen in places where people are more comfortable in that setting.
AFAIK Finland always had more separated sauna culture. They have so many saunas that you specifically pick when you want to go to mixed sauna.
In Germany or parts of eastern europe saunas are popular but there are not that many of them so they end up mixed gender. Also everybody is going to saunas in Finland where as in Germany its much more thing for "fans" or "experienced" sauna goers that maybe accept it as part of the whole thing.
It's pretty common in Australia for people to strip and change at beaches in the carparks .. usually with, say, a car door open so they're partially hidden, often with a bit of towel wrap as a nod toward "decency" - but it's accepted that the easiest way to change from wet to dry clothes is via bit of interstitial nudity.
Depends on beaches, the larger big city beaches often have changing rooms, it's more smaller suburban beaches, country and remote (but popular) beaches.
Friends might arrive together, change together as they talk, go to beach, return, change again, leave - lot's of solo people do it - the only thing that'd be odd would be somebody wandering about clearing having a perve.
This is a bad example. Nude mixed gender saunas self select for a specific part of the population, which is not made uncomfortable by being stared at by people sexually attracted to them.
I would never visit auch a place and neither would large part of the population in these European countries. To be honest I find these places disgusting. And yes I am from a part of Europe where they exist.
The idea that just because nude saunas exists, everyone who wants to go swimming has to be subject to those conditions is ridiculous.
I'm not super comfortable with my body, but I occasionally frequent saunas, and in my experience, there is very little "staring" going on in the mainstream ones (obviously, there are saunas intended for orgies, pickups, etc, but that's a very different culture). Typically, just enough eye contact is made to avoid bumping into each other on the way in or out.
Anthropologically, I've heard that cultural acceptance of staring at people is inversely correlated with amount of clothing worn, i.e. in cultures where people habitually live unclothed, it's considered rude to look at others' bodies.
Of course, I'm old and fat, so I have good reasons for not fearing people being sexually attracted to me…
I don't understand what you imagine to happen in saunas. They are places where you relax yourself or with a couple of friends, you're not there as a showpiece for others nor do you ogle at the fellow saunagoers.
Edit: I saw your other comments, we have no common ground so let's not continue this discussion.
Well, first of all, nothing disgusting about swingers clubs; wouldn’t be my cup of tea personally, but provided they’re consenting adults there’s nothing wrong with it.
But also, like, mixed saunas, generally, aren’t sexual at all. The mere presence of naked people does not imply sex.