Шаги для воспроизведения можно упростить:
var contextOne = new EntityContext();
var contextTwo = new EntityContext();
var user = contexOne.Users.FirstOrDefault();
var group = new Group();
group.User = user;
contextTwo.Groups.Add(group);
contextTwo.SaveChanges();
Код без ошибок:
var context = new EntityContext();
var user = context.Users.FirstOrDefault();
var group = new Group();
group.User = user; // Be careful when you set entity properties.
// Be sure that all objects came from the same context
context.Groups.Add(group);
context.SaveChanges();