Guests are aware when they visit a home that the hosts have boundaries that cannot be crossed.
Guests know or should know that they cannot go wandering about upstairs, looking in their hosts' bedrooms. They ought to be careful in conversation that they do not mention subjects that may cause offence to the host. If the host has strong views on a subject, it is best not to argue with him or her. Guests know that they cannot bring their pet dog to somebody else's home unless the host has expressly said this is acceptable. Even if the host is an animal lover, permission to bring a pet dog must be sought.
It is now recognised by most people that when you visit the home of a non-smoker, they should not smoke inside. If they need to smoke, they should put their coat on and go outside. There are still some people, probably mostly from the upper strata of British society who think it is rude to forbid smoking in one's home. However, this view is very much in a minority.
It is important to recognise these boundaries when one visits a home and if hosts prefer, even if they do not insist on it, removal of shoes, this should be complied with by guests. To ignore this boundary is, as stated in the previous post, taking hospitality for granted.
Some people would object to comparisons with smoking pointing out the health risks of smoking, compared with the minor ill effects to health of wearing shoes past the door. However, it is not so much the health risks that should deter smoking in a non-smoking home. Nobody is going to get lung cancer because a few guests smoked at a dinner party. They are unlikely to even develope a cough because of it. No, the reason one should not smoke in a non-smoking home is simply because the smells and mess are not convenient for such hosts. It is simply impolite. Likewise it is not convenient to impose the dirt and dust of your shoes in the home of a person who would object to it.
Some would argue that it is polite for guests to remove their shoes if this is what the hosts do, but it is impolite for the host to request shoes-off. They feel that it is better to leave the responsiblity of politness to guests. To my mind, this is not quite logical. If guests have the responsibility to comply with the preference of their hosts, then it is surely quite reasonable for guests to make their preference known.
Part of the reason why a verbal request for shoes-off may be necesary is because etiquette is so uncertain and in such a state fo flux on this point. While it may be a good idea to remove one's shoes when one is welcomed by a shoe-less host, as this may be a shoes-off home, such a gesture might be taken as impolite by some. There are some who go shoe-less in their home who would be surprised by guests going shoe-less. It is probably necessary for those who desire shoe-removal to make their wish known.