Rita, I'm a bit aghast at the idea of a sign too.
For me, if a professional visitor comes round they generally keep their shoes on if they're not going to be there for long. I would never stand at the door and demand they took them off.
Friends coming over for the first time for a casual visit like a cup of tea generally step in and say 'Should I take my shoes off?', to which my answer is 'Only if you want to', although I'll almost certainly be in my socks as we're shoes-off. Then the person pretty much always takes their shoes off. The visit proceeds, happily.
If they're at my house for a party or similar and will be milling about for a long time, I resign myself to having to clean the floors and carpets afterwards. I would never ask people to take shoes off in that context (in fact I never ask in any context).
I went to a friendly acquaintance's house recently and when I arrived she let me in and said 'Would you mind taking your shoes off?' I said of course not, took them off, and we had a nice visit. I didn't fume, or refuse, or go away and think less of her or that she was rude or common.
There are some very exaggerated pictures being painted on here, on both sides, of people either demanding visitors remove their shoes or visitors steaming in and refusing to and stomping all over the cream carpets defiantly.
Surely in the actual world things go much more along the lines of my two scenarios?
Because I agree, life is too short to have battles about things like carpets and shoes.