I read through all of the responses so mine is going to be all over the place...
We are a shoes-free home. My home isn't overly "pristine" (I don't mind a coffee cup on the kitchen counter and/or feet - with socks - on my family room coffee table) but I do feel as though shoes are very dirty. I also feel like my home is a "nest" - very comfy and cozy, a place to relax. Shoes, imo, are worn when I am going somewhere, they are not a part of my daily routine. When I am home, it feels bizarre to wear them. I feel it'd be the same as wearing a coat and/or carrying a purse around my house.
Most anyone who comes over (or invited in), knows me well. They know I am a clean freak and they know we don't wear whoes. So, this means they respect us, they respect our home, and they take off their shoes. If they are just stoppingby, they can leave their shoes on. Our main floor is tile and hardwoods so I don't mind vacuuming those (I do it multiple times daily anyway). If they think they're going downstairs (or upstairs!!!) w/ shoes on, they are nuts.
Pets - We only have an indoor dog but he does have to go potty outside so we have a small piece of carpet (leftover from installation) at the door where our dog sits to wipe his paws. If it is overly nasty outside, we grab a towel (for that purpose) and wipe him and his paws). My kids (I know this is under the "pets" part, ha ha) wipe their feet off in the summertime too.
Groceries - I deal the same way - come in through the garage, set them on the floor, remove shoes and transport to kitchen.
OP - maybe have those booties (that Laggie mentioned). I see them all the time at home showings. When we have furniture delivered and/or our carpets cleaned, they always wear them. Buy some and have a basket near the door for people who don't want to take their shoes off.