One person's conservative is another person's radical. I'd say the terms or labels that are generally used lag behind the behavior of those stuck with the labels.
In nudism, the old school conservative, who might actually be old, had his club where he was free from having to look over his shoulder to see if someone was bothered. He believed that only by maintaining a club-type arrangement could he have any outdoor nudity, free from legal harassment. And only by careful screening of membership applicants could a proper atmosphere be assured. Some allowed their clubs to drift towards adult-only membership, eventually turning into swinger clubs. That also happened overseas, lest you think that only Americans let that happen.
The other end of the spectrum, originating with the free beach movements (and perhaps with the streaking fad), wanted public nudity permitted on beaches, with a heavy emphasis on "free." There were some successes but basically the same problems existed but without any membership control and with more public disapproval. Nevertheless, there seems to be more public nudity now than ever, but probably with just as much disapproval as ever, too. Ironically, the original free beach crowd are mostly old now, too.
The left can't be off the charts, of course. Nor does the media require balance, real or otherwise. There's no section here for people who oppose nudity in any form, is there? Does the news today have stories presenting things the way the North Koreans or the Russians see things? And should they? I realize those are extreme examples but they aren't off the chart.
Mostly, though, I doubt that the different camps in nude recreation have the same goals, other that to be left in peace while they're not wearing anything. It's like comparing the RV (recreational vehicle or caravan) crowd with the ultra-light camping crowd. Yes, they both like camping but what they have in mind isn't the same. And most people don't care for camping in the first place.
Here I am writing in English and still have to translate some things.
Anyway, I don't think there is a moral side to any of this, although the anti-nudist assumes that all moral rectitude is on his side. We, on the other hand, assume that everybody else is a little hypocritical. But excluding children is a bad sign.