MRZ, DD's nursery did, they started with numbers and letters around 2 years, if a child showed interest. We spend hours walking home, DD read letters from number plates and street signs. I don't see it as actual teaching in sitting down with flash cards, it is part of general knowledge to me like colours and shapes as well,
DD started with letters in print, but not as learning as such, most children just copied it from a sign in the room or from a book.
Most of DD's year group came with these "incorrect" knowledge to school and I doubt it really is a big problem. 3 months later DD forgot most of the letter names, we saw an optician for an eye test and she gave the phonic name to all letters instead of the letter name. If the parents are going with the school's approach when it comes to learn to read and are consisting in their help, then a child won't get confused. Come Y2, end of Summer term and they started with letter names. I found it even more confusing as the children mixed them up, so trying Dd to spell a word with "E" and "I" in it meant lots of mistakes as she swapped letter names and phonics for a good couple of weeks.
If a nursery or pre school feeds into a specific primary school, then I would assume there is some form of teaching as they know which system a school uses. But most private nurseries used for childcare have children going into lots of different schools, we have so many in our borough, they can't even come up with one style of cursive writing.