For me it would be one of those brief linen loincloths like they wear in Jason and the Argonauts.

https://www.karstensloinclothsite.com/jata.html

Well, consideration goes to not wanting soggy cloth around the my most sensitive areas.

So, naturally my first option would be naked.

Failing that; a backless loincloth just a flap at the front.

Failing that; just two flaps connected by a belt, nothing else between.

If a pouch type garment is insisted upon then I would resort to a rokushaku fundoshi, preferably natural unbleached cotton.

Example: https://www.ebay.com/itm/182810373085

Probably a rokushaku fundoshi.

I've worn stretchy cloth breechcloths in the water myself. They've worked pretty well as long as the belt is water-resistant and tight enough to stay secure.

I do likewise, but mine's are blue and green.
Great for a day at the lake or river or beach.

LCFan

I wish I had a place I could stroll around in a loincloth and not have to worry about others looking at me.

There are some spots at bodies of water here that are known (mostly inofficially) as “clothing optional”. Where one may see loins without any cloth, so to say, who would object to a loincloth instead of swimming briefs?
In Germany it's (still?) more acceptable for a male to wear speedo type swimwear instead of ridiculously baggy boardshorts. So, while a breechcloth may be revealing by today's standards, there were more skimpy briefs to be seen in the 1980s and 1990s.
Of course people will look twice when they see something out of the ordinary. But reactions are few, and negative ones even more so. In the mid of summer some people commented on the “good idea” to wear so little, which I find encouraging.
Mostly I wear a loincloth (other than at home) for water-related activities: swimming, canoeing, stand-up-paddling. I did some short hikes, but mostly it's just the way from the car park to the water's edge (may be a kilometre or so in places).

Yours,
LCFan

That sounds really cool. I mean I imagine something like that hast to exist here in the U.S. but not that I'm personally aware. I have frequented a nude resort but that at the very least has legal approval.

If by “something like that” you mean “clothing optional”, then, maybe, Germany (and Europe in general) may be a tad more liberal than the US, from what I've heard. But even here these places are not universally accepted or even tolerated.

For wearing loincloths, our fellow writer Aaron here seems to be able to find suitable locations at least in his part of the US.

Yours,
LCFan