What are the consequences of a monk eating meat?

This is not a question about being a vegetarian. My question is since the Buddha didn't prohibit monks from eating meat, and since monks are supposed to be easy to maintain and take what is offered, how should/would a monk who has chosen to be a vegetarian handle being offered meat by a lay person? If they chose to refuse the meal would that make them high maintenance, proud or unappreciative? If they ate it, how would they reconcile that with their personal practice? I'm particularly interested in an answer from any monastic on how they have handled or would handle this.