The thing is, everyone always wanted to eat meat - it's good and filling.
The problem is that, before modern refrigeration was introduced, it was very easy for meat to go bad and make people ill. This was very common in warm countries, and so it ended up codified in religious cultures from those areas. Around the Med, it was no biggie: vegetables were pretty easy to grow in large quantities.
However, the type of doctrine that ended up as commonplace in Europe (because of military and economic developments) was a very Northern interpretation of Christianity, coming from places where people had to eat meat because vegetables were hard to grow in cold climates. A lot (or rather most) of the Templars themselves were French or German knights; they came from places were meat was a firm staple of rich diets.
And so most of the warnings against meat went out of the window, never to return. It probably helped that "the Enemy" had gone the opposite way.