I play with a lot of vegetarian sims and most of the time, even with meat meals in the refrigerator, they will get a vegetarian-safe meal when I use the "Get Leftovers" action. It is only when there is nothing in the fridge that is vegetarian-safe is when they will end up eating meat. But if you don't direct them, they will end up cooking their own food. At least this is my experience.
When I first made my legacy game, I made almost all my sims vegetarian but found that it quickly got boring. Consider the "Grand Meal" you make during the holidays: there is only one vegetarian-safe option out of like 5. Not the most ethically comfortable for me, but I now play with both vegetarian and non-vegetarian sims.