Community sure isn't simple in A Day No Pigs Would Die. For one thing, there are lots of different communities, from the townspeople to the nearby farmers to the kids at school. But here's the thing: the Pecks don't really seem to fit in anywhere. They're different because of their religion and because of their strict, plain way of living. So for the Pecks, successful community seems to be a complicated, delicate dance between being "neighborly"—that is, sharing, caring, and other touchy-feely stuff—and keeping juuust the right amount of distance.
The most important "community" in the book is a community of two—Rob and Papa. All the other communities in Rob's life are secondary to his relationship with Papa.
The people of the larger community like and respect Rob's father (as evidenced by the turnout at his funeral), but mostly because their values aren't really all that different from his own.