I’m aware of the conspiracy theories, but that makes no sense. No party with the slightest understanding of foreign affairs would ever go through the embarrassment of giving up the influence and diplomatic connections UN membership offers-- especially just to get away from being indirectly shamed over backwards views on human rights. I feel like Leslyn Lewis (the Tory who sponsored the petition) might even expect any such efforts to fail even if the petition gets enough signatures for a formal response.

(TLDR: it only makes sense as a cynical way for a politician to win some popularity.)