No. You are not over-reacting.

I had something similar happen to me.

Went into a local grocery store and the rent-a-cop very forcefully told me I had to leave my Fatboy at the front desk.

Being caught off guard since this was the first problem I had is the several years I've been carrying a "man-bag", I left my bag at the front desk after pulling my wallet out, completed my purchase with everyone looking at me, and developed a serious case of the reda$$ on the drive home.

There were women there that had purses big enough to fit me and my Fatboy in walking around unchallenged...

Called the manager, found out that was the store policy.

I raised hell, got no apology, and will not be back in that store ever...

Since then, I've been practicing in my head for when the next time someone calls me down for carrying it... if they want my business, then they want my bag...