I must admit, and maybe I've been negligent or a bad guest here - but it's never occurred to me to offer to take my shoes off when entering someone's house. Nor have I ever thought that I would need to request that from someone entering my house.
What do those of you who have work being done inside of your home do? Internet/cable people, plumbers, electricians, painters - do you ask them to take off their shoes, and what happens if they are uncomfortable doing so, or have to have them on as a condition of their employer? Or would you offer them those bootie type things in lieu of taking off their shoes?