I'm pretty sure the answer is
From checking the internet, it seems that the film was but the book wasn't.
Some sources that might help:
Ctrl - F 'danish' comes up with nothing on any of these.
As for whether or not the novel was less controversial, I don't think that even if it wasn't it would have been banned.
Books are less likely to be banned. As long as they aren't religious in religion sensitive countries, then very few books are banned.
There are probably quite a few transgender books, but a film is different from a book. A film is a visual and some countries may not want these images shown, but very few countries will ban (non-religious) books, because with writing you can imagine it, whereas a film you are given the images.