I went to my neighbour's apartment for some beers and an Indian takeaway.
Whenever I visit him, he always reminds me to shut the door and lift the handle up. Once or twice I had not lifted the latch and thus not shut it properly.
Its a simple request, but one that serves a purpose; to keep the door from blowing open and letting in the cold.
There is nothing rude about asking a guest to do or not do something. And there is nothing wrong with asking a guest to remove his or her shoes. You would not be asking them to do something horrible, but to do something they probably do in their own home.