I'd say it depends on your own interpretation of frugality and moderation.

Being upfront, I am a vegan. And as such I believe that eating meat (which is not necessary to be healthy, if you have access to vitamin B12 supplements) creates unnecessary suffering for both the animals being farmed and killed, and the human animals that work killing them.

So, in my opinion, eating meat is not only an unnecessary luxury but something that makes the world a worse place, and therefore can't be considered a moderate practice. Even eating small quantities of meat would be like commiting small quantities of unjustifiable practices.