Are the detectors that stores use at the entrance safe ? Is the type/dosages of radiation they emit a cause for concern ?

The stress of worrying about stuff like this is probably going to do more damage than the EMF/radiation itself. It's literally everywhere to an extent and unavoidable. Obviously ideally we would avoid xrays/scans and keep away from Wifi / emfs at home, especially when sleeping. But other than that I can't see much point in dwelling on it. I used to be obsessed with stuff like this, as well as pollution, and it did me more harm than good constantly analysing and trying avoid these things.

I get what you’re saying about feeling off in stores, though. It could be the detectors, but honestly, it might be more about the lighting or the air quality—big stores tend to have that cold, artificial vibe that messes with some people. I know a few folks who feel better shopping online or at smaller places, partly for that reason.
If it’s something you’re really concerned about, you could always look into alternatives, like shopping online for things you need. Services like https://www.vivint.com/ also make it easy to set up security and convenience at home, which might save you trips to stores altogether.