I am always a little surprised when I see children wearing shoes at home, whether on television or in person. It surprises me because when I was a child, my parents expected me to remove my shoes at the door. When I visited my friends' homes, their parents often expected me to take my shoes off. So it always seems a little strange when I see children keeping their shoes on at home.
The practise of removing shoes was expected until I reached the age of about 12. My parents became less stringent about it as I got older. Occasionally this house rule would be revived in later years. It was restored when I was 21 when my parents and I moved to a house with cream carpets, though they were not consistent in keeping to it.
There are some homes, in the UK, where the hosts will expect the children of guests to remove their shoes, but would not expect it of adult guests. Some guests will insist that their children remove their shoes without removing their own. I can understand why some people may be more concerned about children's shoes; children do tend to be less careful about what they step in and are more likely to run around in long and wet grass. However, adults should never forget that their own shoes pick up an awful lot of less noticeable dirt. There is also the fact that children learn to follow rules better when adults act consistently. There is a certain amount of 'do as I say, not do as I do' in the requirement of shoes-off for children only.
Some childcare experts are of the opinion that children should wear shoes to the minimum necessary and therefore recommend shoes-off indoors for health reasons.