Are men required to be naked in mixed onsens?

I'm going to Japan in April with a few friends and we've been planning on going to a mixed-gender onsen. I did some research and some onsen review sites say that only women are allowed to wear towels while men are required to be naked. Is this true?

It depends on the specific bath. All have their own rules. Some require everybody to be naked, others require everybody to wrap themselves, others require everybody to wear swim suits. Others have different guidelines for each gender. Others don't have clear rules...

If you can let us know the specific mixed onsen you are considering if they donft have a b English website maybe someone can check.
Ifd say as a gruleh in rural onsen in the countryside everyone is expected to be naked. There are some more famous ones eg in Gunma where now women are expected to wear a kind of dress made from towel. Thatfs a big reason for me not to go. Just the thought of sitting in an onsen with a wet towel around me is putting me off. Onsen for me are to be enjoyed naked.
Note also that some mixed onsen essentially end up men only onsen. Which I think is a real pity because sometimes there is a smaller women only one closeby but itfs much smaller and less nice than the mixed one. (In my experience).
Also mixed onsen arenft very common. I know on e on Enoshima (swim wear mandatory. Have never gone S its quite expensive and I never have swimmwear with me) and all the others I know are very remote in the mountains. (Plus those in Gunma I mentioned )

I've probably easily been to over 100 different onsens in Japan and can only ever remember 1 or 2 places that even offered mixed onsens. Both places had mixed and single gender. The same is not always true for Rotenburos but I have not visited many of those.

To the best of my knowledge, women are allowed to wear a modesty towel but men not.

On a positive, you kind of have to search for mixed onsens as they are reasonably rare in general

Ifm not sure youfve got the idea about onsens.
Main point is that you are naked, enjoying the water and the experience (especially in an out door bath with a view).
It can be nice to share that experience with family or friends, and thatfs why there are family baths and (not too many) mixed baths, but if youfre not happy with getting naked with your family or friends then probably the best experience is to have separate baths and to meet up afterwards with your clothes on and talk about how lovely the bathing experience was.