It does not come from those kindergartens, but they may have played an important part in making it popular. The word was first proposed by a linguist in 1966. In the 90s and 00s it started to gain ground in queer circles and from there it spread further. Egalia didn't open until 2010.
Today the word can be found even in official texts like legal proceedings, various texts from municipalities and companies etc. It remains controversial however. See some native speakers disagree over it here: https://www.duolingo.com/comment/5531330