The helmet thing is more about attitude than anything else.
If there's a nice polite sign, then yeah, no problem. I've actually been thanked by bank staff when they've seen me remove my lid as I walk in.
But some people are little hitlers. I've been told to remove an open faced lid when trying to post a parcel and the woman was a right snotty cow. So she got some backchat from me about it.
I've been told off recently for standing just outside the kiosk at a petrol station talking on my phone. (I walked there. Not in the car....) The woman came rushing out, rudely butted in to my conversation with the "health and safety says so" line so I told her top poke it and leave me alone. I was going to explain it all to her when I'd done, but she disappeared in a huff. If she'd have asked nicely and not interrupted I would have nodded sweetly and thought no more of it.
Working as I do with heavy duty health and safety rules in a rather dangerous line of work I KNOW these people are just bullshitting and it does grate a bit. Next time I'll ask to see the risk assessment etc I think, then sit picking holes in it.