There are going to be cases where a player's WAR varies greatly from one site to another, but again, having an understanding of why that happens helps to make sense of it. The discrepancy might create a lot of confusion for some fans, but that is really not a shortcoming of the stat, but rather a shortcoming of the fans who haven't studied the stat enough.
That is not meant to be a knock on the fans who don't care about WAR. Not everyone has the interest to dig deeper into advance stats, and that's perfectly fine. However, if that's the case, it's really not right for those people to blow WAR off as somewhat useless because of that discrepancy.