She could be associating the chip with the mark of the beast...although the much more likely option is that "religious beliefs" is the easiest scapegoat.
I understand that, I just think it's silly that that is the go to objection, not just for this but for a lot of things people don't like. (Her not liking this is clearly justified, don't get me wrong.) Think vaccine's cause autism? Refuse them because of religious beliefs. Don't want to do jury duty? Religious beliefs.