At preschool it was done entirely by age.
Oldest girl was Mary, next was the star, then angels, then lambs
Oldest Boy was Joseph, next was innkeeper, then shepherds, then kings.
It was done in mime with the teachers telling the story, then they sang several songs at the end. I never heard any complaints about casting over all 7 years my dc were involved.
Reception was similar. All in mime with a year 2 narrator, lots of songs. Each child had something individual to do like hold up a picture in a song. Again no complaints.
Year 1 was done by asking the children if they wanted a speaking part or non-speaking part. Speaking parts were either narrators (good readers) or single lines. There was always one child who didn't want to be on stage at all, and often they'd find something like banging coconuts together to be the donkey's hooves. There was usually 1-2 parents upset that their child didn't have lines, often though more upset that their dc had said that they didn't want them!
Year 2 every child was asked what they wanted to be and if there were multiple people for one part it was drawn out of a hat. They did 2 shows with different casts. In ds' year the non-speaking donkey was the most popular part (ds got one of them!) followed by the angels (who sang). So it wasn't always the obvious parts that are popular.
Again never heard complaints.
Juniors was a different kettle of fish. Huge juniors: they did one performance for each year.
They officially auditioned... and then seemed to ignore that. We had the meant to be emotional Mary, acting with all the woodenness of Pinocchio, the inaudible Gabriel (even with the microphone), and that was just one year. The odd thing was, having happened to be in the school when they were auditioning, you could absolutely have predicted that, and were several children who auditioned better. Neither of the children enjoyed doing it, you could tell.
Add to that they normally only had about 15 parts, the other 140 children would be sitting in school uniform with a couple of songs to sing. One year there were more like 30 parts... so they doubled them up, so 15 children got 2 parts. Never understood that. If I had over 150 children, I'd be splitting as much as possible.
140 bored children (and they were clearly bored) in school uniform does not make a good performance.
I remember one of mine (who didn't want a part) commenting in year 6 that all the parts that year allocated came from one form. Guess who did the auditions-that form teacher.
And the performances were generally absolutely dire. The scripts were written by a parent. I think she thought they were terribly funny. The entire scripts revolved round the huge joke "they didn't have X (insert phones/cars/sat nav etc) in the year zero". It wasn't funny the first time. She wrote new scripts for each year ever year, so not sure why she didn't get bored with this. That was the other bit the "chorus children" had to do.
Joseph would say something like "I don't know how to get to Bethlehem, shall I set the sat nav" and the chorus would say "No, they didn't have sat navs in Biblical times." Oh so funny!
Surprisingly the parents tended to gush over this. "Better than a West End show" was said at least once. The only excuse for saying this was if they watched the Play that Went Wrong and thought it was serious.
There were complaints over parts, especially in year 6 when the same children got the parts in the Christmas performance also got them in the summer. I pointed out one year (to the school) that there were only (over the two plays) enough parts for 25% of the girls to have a part at all if they didn't double any. So why were all except one part given to the same children again? Apparently children enjoy more being part of a chorus was the response, and it was so hard on those given parts not to have that experience. 🤨
I used to sit there in awe as how dreadful the performances were. How was it possible for to make such a dreadful performance with the number of rehearsals they had? Truly amazing.