well since it never occurred to anyone to actually as a policeman about this, I did.
In London (the Met police) removal of footwear is left to the discretion of the attending officers. Obviously if it is an incident which requires themn to enter a Muslim home in a hurry, they won't do so. If, on the other hand, it's a visit which means 30 mins or so talking to one or more members of the family, they may well do so out of respect.
The situation in other forces might differ, but I doubt taht it differs by much.
Can't answer on the dog bootees as I didn't see a dog handler anywhere, but I doubt that there would be time to put bootees on one in a situation where a dog needs to be used.