Google Wallet/G Pay/Apple Pay does the same.
And, knowing Google, that's an extra tier to be harvesting and selling your data!
That will throw up a warning on their system, the other shopper looks like they are using someone else's card to pay for their bill, unless the first customer pays in cash.
? They don't check the name on the loyalty card against the name on the payment card!
I don't think you can use the same card at the same time for two transactions, can you? Presumably, if you stop a customer in Tesco who has a Clubcard, they're expecting to use it themselves.
Also, people are so scared of scams these days, they may well think that you're somehow trying to do this to them - even though I don't think it would be possible to do with just a Clubcard.
I suppose, if it's somewhere where your purchases generate extra discount vouchers, you could skew their profile. Ask an elderly person if you can borrow their card, thinking they might appreciate the extra points - then they end up getting vouchers for nappies and baby food instead of the ones for coffee and bread that they might actually want to use!
I like the Scan & Shop/Shop & Go or whatever they call it, but if I need to grab anything for work, for which I need a separate receipt, I have to put it aside and go to a robot till afterwards to pay for it separately.