I do not as a rule always remove my shoes when visiting other people's homes. In Britain, removing shoes is not the norm and might be considered odd or even rude. However, some people would like visitors to remove their shoes, but are afraid to make the request. I should very much like to encourage those people by my behaviour.
Hence, I only remove my shoes if the host is not wearing shoes and possibly not even then if I know they wear shoes at home sometimes.
However, some people wear slippers that look like shoes. This really can cause confusion, Men may wear leather slippers or moccasins that could pass as shoes. It was fashionable a couple of years ago to wear these slip-on sneakers. Some people started wearing them indoors as slippers. At the moment, it is very fashionable for girls to wear outdoor shoes that are identical to slippers. If somebody is wearing those indoors, how am I suppposed to know if they are slippers or not? In the summer, some people may use indoor-only flip flops as slippers.
So people, if you would like people to remove their shoes in your house, but are too polite to say, please wear slippers that look like slippers and leave lots of shoes by the door to make it obvious.
Or better still, just pluck up the courage to say "We remove our shoes in this house." You may be surpised how gracious people will be.