When you tap on "Add friend" on the stars list, in other players' home or after talking to them on the street, a friend request will be sent to the other player. In order for them to be displayed on your friends list, they have to manually accept your request, until then, it is in pending state. It is possible that the other users did not play the game or check their friends list since you sent your request.

Don’t worry though, they will surely confirm your invitation sooner or later. Besides, you can always try adding new friends to expand your list.