That still doesn't sound like the customers fault at all. It should be possible to set certain things as out of stock, depending on the system probably automatically.

The fact that you're interrupted for online orders sounds like your workflow isn't optimised for having online orders at all. Just look at McDonald's drive-in, that's a completely separate flow from the in-store orders usually and they make it work. That might be a very visible example but many other stores have updated their workflow to accommodate online orders if offered.

So both these issues (calling customers to fix shit and the forced workflow) are completely fixable. You shouldn't be mad at customers using delivery services, be mad at the store owner that just wants the money from delivering without making sure their system is up for it (not to mention they underpay you, even more reason to be mad at em)