I had a Author come in with Self Published books that he donated to the Library. The subject matter is questionable. I will pull a tag from amazon on the books. Am I obligated to put the books on the shelf?
You have to develop a balanced collection. You can't ignore non-centrist views. That being said, if it's so extreme that there's little demand, it might not be worth collecting. If a "nonfiction" text is patently false, it might violate your mission statement to educate and inform your members (or whatever it is) unless there's an interest in collecting original sources for research purposes.
Neither of the examples you gave is collected in any library indexed in WorldCat, according to a search by ISBN. If someone came in with that sort of thing here, we have a lot of religious texts but not many books of poetry, so it's possible we'd accept the Watchman book but not the poetry one if it was a local author and met our special "local author" exceptions to the usual standards. (This is why it helps to have a robust policy.)