I think idea was that interpersonal conflict wouldn't exist between the crew. The Enterprise is supposed to be this huge, brand new Flagship of Federation. It's going on a new deep space mission. And only the very best of the best can get a posting on it.
There's plenty of interpersonal conflict with other characters. A good example is season 2, episode 14 The Icarus Factor, where Riker's Father comes on board.
There's interpersonal conflict when Ro Laren joins the crew, too. It's an idea that was often paid only lip service to once Roddenberry was out of the picture.