This is conflicting, on one hand it's certainty within the right of a store to bar people who shoplift, it's really an imperative to do so. The petty crime issue the retailers here are trying to counter is a real one. But this application it feels like falling down an increasingly slippery slope. Sure, today, it's just "send an alert and the store can do what it wants" but how long until that transforms into a de fac…
I'm sure the big three credit bureaux are developing precisely this product.
The stores need not even ban you: they could adjust their prices on a per customer basis to cover their expected risk.
Come to think of it, the insurance companies could get in on the action. The shop gets shoplifting coverage in its insurance package. It prices the tin of soup at $1. You pay $1 because you have a good "theft rating". I pay $1.20 because I have a moderate miscreant rating. The little lcd on the shelf will show $1.20 as the price when I look at it, $1 when you look. The shop keeps $1 from you, $1.05 from me and forwards the other $0.15 to the insurance shoplifting risk pool. Shoplifting claims are paid out of the pool.
And by the way I am a hardcore non-lawbreaker (actually this is true) but it doesn't matter to the shops or insurance companies if I am mis-rated. Everybody wins! Except me.