Only way to be sure is to get rid of your CCW, DL, known address, utility bills, and go off the grid.
Seriously, I think you need to do a better job of articulating what harm you anticipate could happen and then draw any kind of line from "gun store counter jockey saw I have a CCW" to said harm.
If you are in a gun range, it is a pretty good assumption you have a CCW, or would be the type of person to get one.
As mentioned, due to suicides with rental guns, some commercial ranges started a policy of only allowing you on the range if you brought your own gun, or have a carry permit, basically showing that you already have access to a gun and don't need theirs if you just want to kill yourself.
Maybe it was something about that.
Without counter guy's side of the story, it is all speculation.
I've used mine several times even outside of gun businesses because I don't carry around my passport, and occasionally "two forms of government ID" are required. Here it is just another government issued ID. I don't know how they do it in FL.
Also it exempts you from the NICS check here too, so any time I'm getting a transfer they see it then too.