This is very tricky, OP, but I do think now, aged 10, is the time you have to act on the nakedness.
I do get how difficult it is. One of my relatives didn't want to wear pants as they slid into dementia/cognitive decline, but they were still living with the family. It didn't make logical sense to them because they were incontinent, so to them, being in the privacy of their own home, they thought it better not to wear them.
All very logical, but completely unacceptable with children around, even next door's children if they can see this going on, IMO. I don't think it's quite the same as discreet nude sunbathing, as it's all the time and he's making very loud noises, so it's extremely hard to ask other children to look away.
It's the same for any children who have learning disabilities, or adults with cognitive difficulties, disinhibition, impulsivity, dementia and so on.
However, the need for them to remain with a minimum of clothing still remains and I would start on those rules now. You can't go in the garden if you don't have pants/shorts and a T-shirt, even if you want to, and if you take them off, you have to put them back on. That's also the rules for visitors; anyone visits, you have to wear clothes. Reward compliance, consequences for not.
It's much easier to do this now, set these rules, find comfy things to wear, and endure the learning curve now than when he's 13, gone through adolescence, or older, when people's tolerance will be even less than now.
It may be that you never fully get on top of this, and in that case, you are likely that, as he gets older, he will be looking at supported care with multiple carers to go anywhere, given that we can't have adult men wandering the streets without clothes on, whatever condition they have.