Do you know of any class-conscious or anti-capitalist children's songs or nursery rhymes?

Woodie Guthrie has a children's album. Elizabeth Mitchell has a similar spirit. Folk is a home of humble resistance for all audiences imo

Oh the little red hen took a grain of wheat, said this looks good enough to eat…

Look up “the little red song book”

union maid is commonly sung with children

Try to make an a capella version of some punk songs.

Dead Kennedys- Let's lynch the land lord:

"But we can. You know we can. But we can. You know we can. Let's lynch the landlord, man."

Dropkick Murphy's- Boys on the dock:

"Say Hey johnny boy, the battle call. United we stand divide we fall. Together we are what we can't be alone. We came to this country and made it our home."

It's always fun to go "Say Hey"

In french, there is Dansons la Capucine (french link), which is, like many french revolutionary song, based of the melody of the Carmagnole. The Capucine is more destined to children, but still written by a revolutionary (or its grandma it seems).

A quick translation if needed :

Dansons la capucine          | Let's dance the Capucine  
Y'a pas de pain chez nous    | There is no bread at home  
Y'en a chez la voisine       | Our neighbours have some  
Mais ce n'est pas pour nous  | But it is not for us  
Youh !  

Same with fire  

Same with bread  

Dansons la capucine          | Let's dance the Capucine  
Y'a du plaisir chez nous     | There's happiness at home  
On pleure chez la voisine    | Our neighbours are weeping  
On rit toujours chez nous    | We're always laughing  
Youh !  

I always liked Raffi growing up, I don't think those songs have any capitalist or oppressive themes?

Also songs with nature or animal themes, like "And the green grass grew all around" lyrics here- https://kids.niehs.nih.gov/games/songs/childrens/green-grass-grew

And this one by Kimya Dawson and Antsy Pants - Tree Hugger is wicked cute

Sesame Street?? Must have some fun ones

Seconding little red song book, and also just singing songs you like and you can always adjust for the kiddo's interests or whatever

https://fedicy.us.to/Deltarune%20Don%27t%20Forget%20Sung%20by%20Laura%20Shigihara.opus

This indoctrination is creepy as fuck.