Dau and husband wear slippers most of the time in winter socks and barefoot in house in summer.
I always wear slippers in summer, but do normally wear footwear in the house all year. When hot I am barefoot in the house and will go into garden and even cross road to car to get something out of it barefoot.
When entering someone's house I would always take shoes off to be in socks or barefoot.
So the carers might not be placing as much importance on it as you do.
However if you think this would have been important to your wife pre dementia, and it isn't causing her unnecessary distress I do think that you should ask the staff to try and achieve this, however if there are other more important battles to fight then it might be best left.
It is still relatively early days in the care home, and they might slowly persuade her to do things.
Also maybe worth buying stick on labels for shoes so easily identifiable to staff/ other family if in wrong room.
