I'd rather the shop said "no, we can't sell that" then they take the item and just throw it into the trash. That happened a lot when I worked in a thrift shop, because people would donate things that were broken and not safe to use. We were lucky, since we *did* have staff who could repair appliances and bikes, so fixable things got fixed and sold. But the bags of torn and stained clothing, used tissues, school papers, broken toys and the like were really discouraging. The boxes of broken glasses and pottery weren't just discouraging, they were dangerous... and often the contents hadn't been packed so they could travel.

Most thrift shops don't have people on staff who are good at repairs, so they have to say no to all kinds of things that they don't know much about.

Your best bet is to look for a larger shop that does pickups. They'll have an office who can tell you what they take and what they don't take. Often if they can't take something, they'll know another place that can. And a thrift shop doesn't get to be big without having good people who want to help on staff.