Agreed that consistency is very important. However, I think that your #3ers, even though they correctly push their system very hard, are actually behaving in a very irrational way.

Being willing to let inconsistencies slide (as the #1ers and #2ers do) violates the important rationalist rule of noticing when you are (or ought to be) confused. However, it's a much less dangerous response than chasing down confusion but refusing to let the results adjust your moment-to-moment world model! In other words, #3ers are only doing the first half of a scientific or mathematical process, which eliminates most of the benefit, but still is enough to give them a false sense of confidence in their own assertions.

The "fuzzy" thinkers, #1 and #2, are just sitting back and letting society guide them along the path of least resistance, often acknowledging (particularly in the case of #2ers) that they have only minimal confidence in their own knowledge. That's not particularly rational, but it at least isn't actively pushing things in a bad direction.

I guess to put it another way: not all changes make things worse, but anything that makes things worse must be a change. The volume of choice-space that makes the world a crappier place is much smaller than the volume that makes things better. Because of that, overconfidence can be much worse than underconfidence, though both are bad.