I think you way over reacted to a security guy just asking you to open your coat. Does the store do this to everyone, or every third customer, or only in the middle of the night, or whatever? You're in their store -- if you don't like their security measures, take it up with management or don't shop there or both.
Getting nasty with the guy at the door neither proves nor solves anything -- he is doing what he is told to do. When I was working, it was my job to do what I was told in keeping clients (long time or new)at bay when the boss didn't want to be disturbed, and I took a lot of crap about it sometimes. Nevertheless, I didn't have any option but to follow instructions if I wanted to keep my job. Getting nasty with staff never gets you anywhere. They care more about keeping their jobs than about whether you are happy about it or not.
Some stores here make you leave big coats, parcels and big bags at the door and not bring them into the store. I wouldn't like it if I were accused of shoplifting, but all the security guy did was ask you to open your coat. It's the way the world works nowdays.