I do worry that we're all going to drive ourselves, and now our children, mad with obsession on what are almost certainly minor points of hygiene. Washing hands frequently is just sensible as we rub our face/eyes/pick nose all the time and it's a nice short hop for the virus to get from one snotty-nosed child's hand to another.
Washing clothes is another remove, and I'd argue also fairly pointless. If a Covid-infected child sneezes or coughs all over another one, including on their clothes, then that child is fairly likely to get it. They're already infected inside, washing the clothes is shutting the stable door after the horse has bolted. And it's not as if pupils are coming home after a 12 hour stint in A&E, where I'm sure HCPs are extremely careful about changing, not travelling in work clothes etc.
However, thinking back to when I did my fortnightly supermarket shops at the peak (wearing a handmade mask, my glasses, Vicks First Defence spray up my nose and sleeves pushed back - see, I've also been fairly neurotic 
but I think more justified back then) I did often put my supermarket clothes in the wash and would spray my bag/coat with Dettol 'All in One' disinfectant spray (it can be sprayed on fabrics and sofas, and claims to be anti-viral as well as anti-bacterial). It made me feel better and I do see that these suggestions to shower and throw everything in the washing machine are for reassurance. They probably won't make much, if any, difference to transmission though. But for those mentioning blazers, the Dettol spray seems sensible, I suppose.
I really worry about the effect all these extra disinfectants are having on the environment, though. 