I don't know why people are laughing at you. I am in a country where "non-essential" shops are closed, I have a toddler who is quickly running through shoe sizes. I've had to order him some socks on amazon and hope they turn up/fit. I noticed the other day the elastic is going on a lot of my pants, so I could do with some new ones. No idea what size to buy online, in a shop I'd take a pair out of the packet and be able to hold them against my waist. DH commented he's in need of new shoes. I've moved from my winter boots to my shoes and realised that they aren't really in good condition any more and could do with another pair. (Neither of us are especially fashion conscious, so yes, we do only have one pair of shoes :o)
Friend needed to replace their washing machine recently. In a house with 2 under-5s, a washing machine is an essential (using a laundrette also quite risky in terms of contact, and probably having to take kids with her) But no, electrical appliances are not essentials, so the shops are closed. She managed to get one, but it was tricky. Her child also outgrew their current car seat and needed a new one. You can buy online, but it's recommended to get in store so that the fitting can be demonstrated.
However, even though non-essential shops are closed here, supermarkets are open. So in the UK at least, you'd be alright for children's clothing, shoes might not be the best quality but they will do (in fact the Asda "little walkers" toddler shoes are brilliant quality). Our supermarket clothing here isn't quite as nice. But I might be lucky and catch the shoe week in Aldi.
Not stockpiling as such, but yes, if your DC are on the cusp of needing new shoes I'd get them some sooner rather than later.
Things like uniform wouldn't worry me, because if everyone is in the same position, the school isn't likely to be bothered about it, but ordinary things like art supplies and looking at the fit of clothing is surprisingly annoying to be without!