If everyone in your town is related to you - you're one big happy family - you're going to have a few mutants, and a few family feuds. Otherwise, you'll be just like any other community of 2000 people.
Yah. There is a bit of a fiction that "blood relation" means a whole lot beyond your nuclear family. It doesn't - level of genetic similarity falls off *quickly*, and then your relations are governed largely like they are with any non-related human - by the details of interaction, not by blood relation. "One big happy family" only happens if the people within it are, in fact, nice. How often do you get a group of 2000 nice people together in one place, much less have them all live together permanently? The fiction that family = happy seems to do more harm than good, honestly.
And, as has been noted, long lifespan gives us a resource problem. If it doesn't come with a post-scarcity culture (one in which food and energy resources are so cheap and common as to be negligible issues) then population growth becomes a massive problem. We are overburdening the planet as it is. Imagine how ugly it gets if nobody ever died to make room for new people.