If asked to remove their shoes, most people are polite enough to comply. However, it is always possible that there may be some refuseniks.
If somebody refuses to remove her shoes, the host has several options:
1. Not let them in.
2. Let them in, but express one's unhappiness. Not invite them in again.
3. Let them in, express one's unhappiness, but invite them again hoping that next time they will comply.
4. Let them in and say nothing. Not invite them again.
5. Let them in and say nothing. Invite them again in hope that next time they will be more polite.
There is not right or wrong response. Whether you let them in and whether you invite them again entirely depends upon your wishes.
You have every right to refuse to admit somebody to your home. If a person is visiting to sell you a product or service, or to promote their religious organisation (usually Jehovah's Witnesses are polite enough to offer shoes-off) then you might well refuse to let them in. On the other hand, if your boss is visiting, it might be a bad idea to refuse to let her in!
If the visitor is not a close friend, but a person you have invited to dinner in order to make close acquaintance with, you have every right to never let them darken your door again. On the other hand, you may not want to loose a close friend over the issue. However, you might feel more comfortable expressing your unhappiness to a close friend than to a occasional visitor.
There is simply no right or wrong response to refuseniks.
Would you let somebody in your house if they refused to remove their shoes when asked?