Why do Japanese commonly steal the folk lore of Baba Yaga for their own...

Because they didn't,you seem to be a bit confused.There is no BaBa Yaga in Japanese folklore,there is a character that is slightly similar but her name is not Baba yaga,and there are similar characters to Baba Yaga in the folklore of many other countries and cultures around the world as well.
 
Folklore is like seeds. It travels with the winds bringing tales of good and bad, funny and sad .
Then it grows into the peoples' lives.
 
Baba Yaga is Slavic! first off, and when did they do this?
....what's that I hear? a mortar flying along and a pestle scraping and pushing it!
if that's true be sure someone is getting their skull boiled and hung on a fence!

Baba Yaga scared the stuffin out of me as a kid!
 
I have seen absolutely nothing in Japanese folklore that remotely resembled the Russian legends about Baba Yaga... Actually The Movie "Spirited Away" did have some Baba Yaga esk twinge to it didn't it.
 
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