It was not a good sign for Dulcie to be rude to General Kitchener. And then she turned Benvenuto Cellini face downward with a severe gesture. But that was not inexcusable; for she had always thought he was Henry VIII, and she did not approve of him.

What does 'she did not approve of him' mean?

What does 'she did not approve of him' mean? She did not think he was a good man, she did not think his conduct was acceptable. I don't approve of a person who eats with their mouth open.
It means she did not like him or his ways/manner of doing something.

For example: I do not approve of the way he talks

This would probably the man talks rudely and I would like him to change his behavior.