I think that when something runs contrary to established science, it doesnt just mean different on the surface, but fundamentally different. Not so much different in content, but rather in how it was arrived at.
Such that the definition of science includes a framework that allows for new and better ideas to emerge and replace old ideas on grounds of merit, such as more accuracy, elegance, evidence, ability to make predictions and so on.
It is that respect for the ethos and method of science that makes the subject what it is, and thus no place for content that doesnt hold that respect.
If a physics teacher turned out to be the Einstein in a Newtonian Paradigm, i would think he could still tell students sincerely about his interpretation and still call it science as it was arrived at by scientific means. But in all honestly he might be better to publish that first and put it out there to challenge the status quo. He still has a duty to teach Newtonian science as the mainstream foundation untill his work meets the global peer review and testing, which is an important part of the scientific method.
Thats different to someone advocating the truth of claims that have nothing scientific about its claims, and to insert it into scientific curriculum posing as on a par with chemistry, biology and physics. This is what i would understand as 'contrary to established science'.