I'm curious, I've never read Birthright. Do they show Superman eating eggs or cows milk that you can say he is a vegetarian and not a vegan?
He specifically states that he is a vegetarian (and as I said, he wears leather, something a strict vegan wouldn't do). This is because his senses allow him to perceive the energies given off by a living being (a concept first proposed by Elliott S! Maggin in his classic Superman novels), and the sight of dead beings feels wrong and empty to him.
And I don't understand why some people react negatively to that idea. I mean, he's Superman. He's the embodiment of reverence for life. And it's an established trope that his sensory abilities are practically limitless. It seems logical that those would be connected, that he'd value life so highly because he can perceive it -- and its loss -- on a far more profound and intimate level than humans can. And it seems logical that someone with that kind of perception, and that kind of connection to life, would be a vegetarian.
Leather is as much of an issue for a vegetarian as a vegan. You can probably find vegetarians and vegans who don't wear leather and vegetarians and vegans who do. The names only referring to eating.