The "rule" I was told was outerwear (jackets, coats, etc.) was to be removed... whereas suit jackets, etc. were not.

I've been asked to remove a suit jacket a couple of times. I generally wear a sleeveless shell underneath and will usually just partially slip off the jacket and say "I'm not appropriately dressed without it" and they will let me walk through with it on.

I do not think it is appropriate to force someone to walk through in spaghetti straps because of a cardigan... what if they had just a bra on under a cardigan? Is that appropriate too?