This is presuming that the "protein resequencer" technology at the time wasn't able to make a chunk of raw meat that could pass as prime rib, once suitably prepared by the mysterious Chef. It was able to make chicken and meatloaf after all, per Memory Alpha. Regardless, for the size of the ship it would certainly have enough space aboard to freeze several head's worth of cattle, or enough to feed her crew of 87 with beef dishes for at least the first year of the voyage; "Desert Crossing" in which Trip references the meal is some ten months since they left Earth.
Anyway, as to whether or not humanity has gone vegan - I would hardly think so. I've always assumed that replicators and their equivalents were a luxury aboard starships that would save everyone the hassle of carrying all sorts of foodstuffs around with them, and the facilities to prepare them. On Earth in the 22nd century, the population's diet would consist largely of local sustainable meats and agricultural products, helped along by various alien technologies (as suggested in "Broken Bow"). By TNG, Keiko's surprise in "The Wounded" that Miles' family prepared and ate raw meats suggests that by then few people prepared meats at all, and would at best head to the supermarket for some prepackaged raw stuff. Humanity has always enjoyed the preparation of food and I hardly think we'd move wholesale to a TV dinner society if we could help it. Ask the Siskos.
Mind you, twenty years ago as a starving student I might have liked nothing more than a Chef Boyardee can of ravioil... But these days though I'm much happier making my own rice and slicing up a steak or pork chop or even stir frying some noodles to go along with that and my salad.