A luxury is something pleasant or enjoyable but not strictly necessary. It's not a matter of how much more enjoyable it is but just that it can be functionally replaced (Lambo -> Toyota Corolla; Designer bag -> any other bag; Meat -> Plant proteins). Unless there's some rare medical condition that prevents eating anything but animal proteins, we have the means to replace it (as a massive commercial industry at the very least).

WRT alternative diets it really depends on what you replace it with. I believe there are technically some entirely vegan diets without supplements but if you're buying your meat from the store you could just as easily buy supplements from the same place and not worry about it.

I went meatless recently and even as an unabashed meat lover it really wasn't that bad. Vegan/vegetarian meat substitutes have advanced a ton in the past few years when I do get the craving, but I don't notice a day-to-day difference. The main annoyances have been limited restaurant menus and rebuilding my recipe catalog.