I've got laminate flooring but we still take our shoes off and slippers are near the door. My parents are the only ones who refuse to take their shoes off and we end up arguing over it but hey ho...
I think that it's very unwelcoming to expect visitors to remove their shoes to enter your house but I would expect anybody with mud-caked footwear to remove it.
It's very thoughtless. My OH came from a family where everyone had to remove their shoes indoors whatever the weather, when we first got together I thought it was over the top and made me angry but that's the method we've stuck with so second nature to me now.
There doesn't seem to be much concern about it with wooden or laminate floors, that puzzles me, because the grit embedded in the soles can but large scratch marks in surly.
If shoes were really muddy, I *might* ask, though I have a dirt trapper mat and hall runner. I've left a fair number of grass clippings from the park on them myself.
I would ask them to wipe their feet, but not to take their shoes off.
Floors are meant to be walked on, and if you have an impractical floor covering, then that is your fault.
I have a porch with a a mat to wipe feet. If they were caked in mud I would expect them to be removed. Or just don't come round if you're muddy. I wouldn't let anyone sit on my sofa if they were muddy either.
Cloverjo; For the entire duration your visitors with muddy shoes on are in your house, it would be nigh on impossible not to keep looking at their feet. You wouldn't need to say anything :-))
If it was a wet muddy day, the dog and I would probably already done our worst so I would be concerned about what visitors might pick up on their socks!