[HornyMolly]

avoiding eating the flesh of living things,

Don't think we eat "the flesh of living things",maybe once living.
Ok one of the main considerations of Buddist is the Intent. My understanding of a alms round (pidapat) is to refuse nothing,in the form of food.
The intent is to cause as little bother to the doner as possible. We can encourage a donor not to give us meat but if it arrives in the bowl,well it's a done deal. It is thought that to create a scene about a particular type of food could embarrass the donor.So don't do it.
Second point, the cruz of a monastic life is to simplify as much as possible.To not carry around our prejudices,...insisting on vegetarianism is just another prejudice,ok it is more skillful but its still something else to carry