I've heard that this is because people who try to eat fewer animal products usually end up with about the same diet they had when they were not trying.

I find this hard to believe, knowing several people who have become vegetarians and vegans and hardly ever eating meat myself. Do you have any support for this claim? Anecdotally, one new vegan (from being a vegetarian) stopped eating pizza which had previously been more-or-less a mainstay of his. My sister became a vegetarian as a kid despite actually quite liking meat at the time; not only did her eating habits changed but that of my entire family did significantly. My parents describe it as going from thinking "What meat is for dinner?" to thinking "What is for dinner?" ever night.