As for Ancient Greece, some claim that Pythagoreans did not eat meat and some vegetables because of their beliefs about the souls (though others say they weren't vegetarians and ascetics but only abstained from certain types of meat and fava beans). Their school continued its existence in Roman times, so we can conclude that if there were some vegetarians in Rome, at least part of them would have been Pythagoreans.

Hope I gave you some food for research.