Similar to MogBeoulve, I've always headcanoned the farmer to be a pesco-ovo-lacto (or even just pesco-ovo, with how I often play) vegetarian. Maybe for personal reasons, maybe for medical reasons. Either way, the stuffing and cranberry sauce they make at home fits their dietary restrictions, but the ones at the feast of the Winter Star might have meat, meat-based broth, or gelatin in them, so the farmer doesn't eat it. Marnie is the same, as are some of the other younger members of the town (like Elliott, Leah & Emily). Evelyn is a strict lacto-ovo vegetarian. This is why the farmer eats Evelyn's cookies without hesitation.
Over the years, most of the town has learned enough from Marnie and Evelyn that they know which recipes they can share with the farmer as they befriend them now. Gus makes sure to include several options for everyone's dietary restrictions in the saloon menu, and makes Survival Burgers in addition to meat offerings at the fair, because he likes to feed everyone. Evelyn needs to be reminded every year that the burgers are vegetarian.
This is connected to my headcanon for why Marnie is always the one stirring the 'pot luck' soup at the luau. When she was younger, she asked about the ingredients in the soup to make sure she could eat it. Wanting to ensure everyone could partake in the community soup, everyone asked her to stir for a few years so she could offer guidance when they added their ingredients. She really liked knowing exactly what was in the soup, so she asked if she could keep being the stirrer (everyone traded off previously) and then it just became tradition.