Do believers have the same mindset toward reality?
Belief in the supernatural allows one to abandon all formal logic; do theists have the same mentality toward everyday, natural life too? If no, why should the two be any different?
Let's look at it like this: An unbeliever and a believer are both walking through a maze (separately), blindfolded. Neither have been through it before, nor do they know what they'll confront or how to respond to it when they do.
The unbeliever is alone, feeling their way through the darkness. If he/she is confronted by a threat (attacker, etc.), who will help him/her? And if he/she continues walking in circles, who will guide him/her?
The Christian, on the other hand, is not alone, for the creator of the maze is guiding him/her along the way. Does the Christian wonder what he'll confront? Sure. Does he fear how he'll respond? Of course. But still, the one guiding him/her through the maze is trustworthy.
Some may even say that the Christian's blindfold is removed, though still lost in the maze...but again, being guided through it by the Master of the maze.
Technically speaking, in the sense of "logic", it's not that it's abandoned, but more like transformed. Your own unbelief is evidence enough that nothing God does or has done in Jesus Christ is considered "logical". But you see us as abandoning logic because it's no longer the same logic...it's been transformed.
For the scripture even tells us God's intentions were to make the foolish wise and the wise foolish.