Re: students – I don’t think it’s to stop shoplifting per se (though that probably also happens), but just to prevent loitering. If just one or two people walk in, it’s probably because they need to buy something. If ten high school students walk in, 9 of them (or maybe all) are just causing a ruckus and aren’t real customers.
So it’s not really intending to be discriminatory (like the ethnic examples people gave), at least not against a group. It’s just trying to ensure that only legit customers come in. Arguably, no loitering would be less imflammatory, though perhaps the historical artifact is that students is a good proxy (maybe even more effective, if students tended to heed the n students sign more reliably than no loitering).