My 2 sons are in a local nursery/day-care where there are a number of kids from religious families, but the majority are not. It’s similar to a JCC in the US – the food is kosher, they do the holidays, etc., and it’s fine for little kids.
Every week, they do a ‘mesibat Shabbat’ – a Shabbos party. One boy gets to be the ‘Abba shel Shabbat’ and a girl gets to be the ‘Eema shel Shabbat’. They make Kiddush and Hamotzi, and sing some Shabbat songs. A while ago, the teachers told us that they were impressed that my 2.5 year-old had caught on to the Shabbat songs so quickly, even though he didn’t know the weekday songs. Well, duh!
The interesting thing about this is the uniform of the ‘Abba’ and ‘Eema shel Shabbat’. The Abba wears a kippah and the Eema wears a mitpachat (tichel, kerchief). I find it fascinating that this is the norm in a mostly chiloni gan with mostly chiloni teachers, but that the rhythms of Shabbat are not only valued but completely rooted in traditional structures and roles. It basically reinforced my distinction between religion and Judaism, where Israelis are generally very positive about the latter, but are increasingly frustrated with the former.
Of course (yes, the ADDeRebbetzin asked), if the kid doesn’t want to wear the kippah or mitpachat they may opt out, but it rarely if ever happens.