I shop all the time in Dublin city centre with a backpack on no problems. I know one small bookshop that asks you to leave bags behind the counter, but that's it.
Large supermarkets and electronic stores on the continent that I've been in have different methods.
A Decathlon in Paris takes every bag and holds them in a small closed cubical with a clerk. I think they put them in sealed bags. Another shop lets you drop your backpack into a large clear plastic sack and then you seal the top yourself with a plastic heat sealer that the bags are attached to - a 10 second job and you keep your bag with you.
An electronics shop I was in near Marbella, Spain had a rack of lockers inside the entrance, beside a security guy. You put your bag in, lock it and take the key, and take your bag out on return (no cash or tokens required).
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Americans: please don't lose the "War on Terrurism" (tm)(Copyright FoxNews and the Bush administration) by letting these a$$holes take away your essential liberties. It saddens the rest of the world to see a once great democratic country fall so hard and so fast. Be assertive about your civil rights. Don't accept bull***** like this in stores or on the subway. Don't accept voting fraud in the next electron. Don't give in to the orchestrated "keep 'em afraid" campaign from your government.
Bah, I could rant all day. Please be assertive and stand up for yourselves, against your local store clerk and against your government. Your forefathers wrote the Constitution in a very clear manner - know it and love it.