I don't think it's unreasonable at all. In fact, I do believe that even in nudist clubs residents are required to take extra care with hygiene.
EDITl: I did a little digging on Nudist etiquette and it's seems the common practice is for people to either use a dry towel, when sitting on furniture, or to bring their own seating. Clearly there is an issue with nudity and hygiene.
There is etiquette, but that's very different from there being a known issue with nudity and hygiene. There might be a perceived issue, but that's far from establishing it as fact.
Has anyone ever caught a disease from sitting on the same furniture as someone nude? Given the number of nudists, if there was a significant problem, you'd think there would be lots of known cases. And with beachwear (and swimwear) being so minimal, is there really any real difference between sitting on chairs recently occupied by nudists, and sitting on chairs occupied by people wearing thong bikinis?
This catching diseases from nude people looks a bit of an emotional, not a factual, response to me.
May I also suggest that people in enclosed spaces (eg. the tube) might feel rather uncomfortable being forced into physical contact with a naked body. It's bad enough when someone is fully clothed. I feel this applies particularly to children.
That's because people have old-fashioned attitudes. Some people don't like sitting beside big "tough looking" hairy men, gossiping teenagers, people with large numbers of piercings in odd places, etc.. That's their own issue and no reason to ban big "tough looking" hairy men, gossiping teenagers, and people with piercings from public locations.
My first experience of public nudity was attending a music festival in my early teens. It only took days before it become completely natural to see people wandering around in the buff.