There are plenty of vegetarians who are Republicans. While most I know aren't vegans but lacto-ovo vegetarians (myself included), you don't have to be a whacko lib to live without meat.
I was brought up Seventh-day Adventist, a fairly conservative religion that advocates good health practices, including no alcohol, smoking, preferably no meat.
I can't stand the stuff myself, having been brought up in an SDA ghetto where it wasn't really served anywhere. I made sure my kids like it, though I don't cook it at home, however.
As for the vegans, the few of those I know are more religious fanatics than hippy-lib types. If they vote at all they vote conservative.
There are healthy ways to eat meat and to not eat it.
I knew a lady in my old neighborhood who's family lived in Africa during her childhood, so she was used to living as a vegetarian. She was actually a very large woman.