Sometimes is my fence-sitting answer.
A well-written genre novel (mystery, SF, romance) can pull me in even if I disagree with the political slant to the book–ie the way social class is accepted, questioned; the analysis/reference to current affairs.
A non-fiction text, well, when I disagree with the author here, the disagreement is more likely to have me throwing the book across the room, so I pick my non-fiction books with a greater eye to the author’s likely sympathy with my world view. It’s all very well to be challenged–I don’t look for my reading to enrage me.
Beyond political sympathies, if a book is nasty or snide, I put it aside.
But back to the original question–the author’s political views.
As authors share their opinions/lives on the Net, you can get a fair sense of their world views. I suspect this influences me less than the quality of their work (and I acknowledge the sneakiness of this answer, because “quality” includes for me a style that excludes offensiveness).
So I haven’t really answered the question, but it’s an issue I’m considering–How much sympathy of world view/experience must there be between authors and their readers?