My 10 year old grandson has been avoiding school because his father (my son) doesn't support some material in schoolbooks which he believes is political, not information. My grandson is embarrassed because his father writes in his textbooks. My son is correct in his judgment, I believe, but his strategy has set up tensions and he's concerned about how to get a good education for his son.
When in Rome...
A child's textbook is not the place to stage a protest against the school's curriculum. As you have already observed, it will only cause stress and embarrassment, not actually teach a better lesson.
At 10 years old, your grandson is more than capable of understanding that people sometimes disagree on a subject or say things for a different purpose than they claim. As such, it's not necessary to literally overwrite the lessons in the textbooks.
Instead, the father should encourage his son to learn and understand the textbook as an exercise and a way to understand what other people may believe about the world. At home, he can provide this context and spend some time with his son teaching the preferred alternative lesson.
I know you've carefully avoided mentioning the subject or which side you and your son are on. Still I feel I should discuss that a little. Whether it's Creation vs Evolution or Climate change vs Hoax, there is a lot of basic science underneath, that your grandson may need to successfully complete a higher education.
If your grandson is taught to reject all of that science because it produces some results that are in conflict with your views, it will hurt him badly should he choose a technical or scientific career. It's better to teach him that science works and he should learn it, but it's only as good as humans can understand. Science doesn't produce fundamental truths, but "This explains all the stuff we're seeing, so we're pretty confident that's how it actually works." truths. They are subject to change and limited to what we can observe and understand.
Teach him to investigate, understand and question things, then make up his own mind, and you'll do well by him, regardless of which subject or side you are on.
What your son is doing, without realizing it, is using your grandson's education and well-being as a pawn for his own political agenda. If he wants to teach his son critical thinking skills, and wants to discuss and examine why his son should keep an open mind to alternative perspectives on issues that are, possibly, subjective, that's fine. To use him as a proxy like that is more selfish than helpful. If he has concerns about whether the content is objectively legitimate, then that can be raised. Usually, when it comes to politics, it's more about being stubborn when one's own viewpoint isn't championed.
You should have a serious talk with your son to make sure that he takes his parental responsibilities more seriously. He is behaving in a way that clearly causes damage to his child (your grandson).
If your son doesn't agree with school policies or the materials in his child's schoolbooks then he should take it up with the school officials.