Health services are not really affected by loi 96 and mandarin speakers have no issue talking to their doctors in my experience (specifically living with a mandarin speaker in Montreal in the past, with whom I'm still in contact).
However, doctors now have to be able to communicate in French and English along with any other language they wish.
Independence sentiment in a province annexed through war, even if it was long ago, and that has kept a different identity, has very little too do with racism it seems to me.
As someone who lived in Canada but isn't Canadian, there is so much disinformation regarding Québec in the rest of Canada, and not uncommonly outright hate, that the often heard claims of racism are very ironic.