She could also be using the word because of the links with radical feminism; however, I don’t think she is using the word with that meaning.
She could be. Many uses of radical are in the sense of "root" - "radically different", "radical change" - different roots, changing at the roots.
That's just been misinterpreted through "oh, well, given those uses, radical just must mean 'extreme'".
I think sometimes you get a play where both meanings are possible, leaving it to the reader, eg "the radical notion that women are people".
And I think this could be like that. (Not sure writer's normally get to choose their headline though - might be overthinking this!)
Both these books are trying to get at the roots of the trans belief system. From a believer, and a non-believer's point of view.