Truth of the matter is that most, not all, of the old schoolers or traditionalists are older, and most of the people who really embrace sabermetrics are younger. I think it's that way with most things in life, not just baseball.
When you've believed something all your life, like batting order really matters, it's hard to accept that it's simply not true. You are going to stick with your old school views that a manager must switch the #4 and 6 batters. However, if you came into baseball hearing how negligible such a switch is, then you're more likely to accept it.
FTR, I'm no spring chicken. I was really not even aware of sabermetrics until about 2009, until I was having a debate about Ryan Howard versus Albert Pujols. The guy I was debating with opened my eyes to a whole new world, and I have not looked back. It makes so much sense to me.