Even if we accepted his religious freedoms argument he cannot engage in harassment targeting students for hate, bigotry and discrimination on the basis of his objection of their gender identity status. That falls under prohibited conduct/harassment in the equality act.

Here's a ruling in a workplace tribunal that covers the exact same grounds, and dismisses them one at a time. The exact same principles would apply in Burke's case.

Specifically were likely to cause offense, have the effect of violating a transgender person's human dignity and fundamental rights, creating a proscribed environment, subjecting a transgender person to less favorable treatment, and breaches the Gender Recognition act of 2004 (GRA). It would also create a hostile education environment.