When I was in HS, very few if any teachers stuck to the textbook so closely that they taught everything in it, and nothing else. Some teachers barely used the textbooks at all and just drew up their own lesson plans from scratch, the majority used large parts but not all of the textbook and added some self-made things or stuff from other textbooks.

Of course we too have standards detailing what ought to be taught in a given course, but those really don't go into that much detail, and I'm not aware of there ever being political controversies about them (controversies about them being unrealistic and generally annoying are frequent enough, though ).