No human person has, so far as I am aware, managed to eradicate all irrationalities from their thinking. They are unavoidable, and this is particularly distressing when the irrationalities are lurking in your brain like rats in the walls and you don't know what they are. Of course you don't know what they are - they are irrationalities, and you are a rationalist, so if you had identified them, they would be dying (quickly or slowly, but dying). It's only natural for someone committed to rationality to want to indiscriminately exterminate the threats to the unattainable goal.
But are they all worth getting rid of?
It is my opinion that they are not: some irrationalities are small and cute and neutered, and can be confined and kept where you can see them, like pet gerbils instead of rats in the walls.
I'll give you an example: I use iTunes for my music organization and listening. iTunes automatically records the number of times I have listened to each song and displays it. Within a given playlist, I irrationally believe that all of these numbers have to match: if I have listened to the theme from The Phantom of the Opera exactly fifty-two times, I have to also have listened to "The Music of the Night" exactly fifty-two times, no matter how much I want to listen to the theme on repeat all afternoon.
Does this make any sense? No, of course not, but it isn't worth my time to get rid of it. It is small - it affects only a tiny corner of my life, and if it starts to get in the way of my musical preferences, I can cheat it by resetting play counts or fast-forwarding through songs (like I could get around the chore of feeding a gerbil with an automatic food dispenser). It is "cute" - I can use it as a conversation starter and people generally find it a mildly entertaining quirk, not evidence that I need psychiatric help. I have it metaphorically neutered - since I make no effort to suppress it, I'm able to recognize the various emotional reactions that satsifying or frustrating this irrational preference creates, and I would notice them if they cropped up anywhere else, where I would deal with them appropriately. I also don't encourage it to memetically spread to others. I keep it where I can see it - I make note of when I take actions to satisfy my irrational preference, and acknowledge in so doing that it's my reason and my reason doesn't make much sense.
In short, I treat it like a pet. If it started being more trouble than it would be to root it out of my brain, I'd go through the necessary desensitization, just as I would get rid of a pet gerbil that bit me or kept me up at night even if this meant two hours each way on the bus to the Humane Society.