I'll grant you that it's not unthinkable. But I think it's highly unlikely that there's any kind of non-spurrious correlation between cleanliness and crime.
I find it just as plausible as the idea here that it makes you more morally judgemental of others. If it makes you more judgemental of others, it might well make you more judgemental of yourself.
I don't know if we can necessarily cut street crime by handing out free showers to bums and thugs. Might be worth a try.
"Clean people commit less crimes." Not unthinkable.