I see Gender Ideology as the social contagion. The idea that gender is a construct has become a social contagion due to its spread from academia throughout society.
And the idea that many aspects of gender are social is indeed the current scientific position, so dismissing it as "ideology" is what strikes me as an ideological position. Generally, men and women express themselves in, say, Thailand and France differently from how men and women express themselves in Saudi Arabia and Ghana. I'm not sure why this would be a novel or radical idea.
I sure as heck don't want elementary school teachers deciding! Since when did mere school teacher become experts in gender studies, enough to determine a condition that is not clear to many EXPERTS.
Where does the ruling imply that teachers have to decide anything? They simply don't have to tell parents about a child's gender identity. Said identity could be a result of transitory exploration or a more deep-rooted and permanent source, such as gender dysphoria.
Problematic parents will always be problematic. This particular topic is getting under the skin of ordinary, average people and invading their sense of propriety, fair play, trust etc... Parents send their kids to school to get an education not to be made into someone's "science" experiment.
I don't know how all of this follows from "teachers don't have to tell parents about a child's gender identity." I see no experimentation, indoctrination, or any other sinister plan in this case.
Also, many parents have no problem exploring and talking with their children about the latter's identity. If the people you're describing as "ordinary, average people" dismiss psychology and science in favor of calling the unfamiliar a "delusion" and suppressing it without much or any discussion, it sounds to me like the problem may not be with the schools.