How do you convert someone, ie a close friend, away from irrational thinking, without offending them?
Perhaps this is why i am losing friends like i am losing my hair?
Or why intelligent conversation is now reduced to talking, irrationally, about the weather?
oh woe is me and my bloomin enquiring mind 
If you are losing many friends, maybe your thinking is not as rational as it could be. What is irrational in your opinion? If indeed you are losing friends because of some objective standard of irrationality that is being breached, then what in you causes you to select these friends? Either way, there is room for reflection here.
Throw out an example for discussion.
A lot depends on how you broach the subject.
If there is an argument and you’re trying to get someone to admit they’re wrong or their reasoning is wrong…that’s near impossible.
You’re better off explaining how you might reason out the subject, and what conclusion you would reach, and see if they can agree with that. Don’t draw attention to any differences between this and what they said previously.
stop
There is one answer if you are a parent, another if you are a teacher or professor, and a third if you are a spouse. Otherwise, the answer is that this is not your place. If you’re concerned that the beliefs are harming the individual in quesiton, you may mention it once to their spouse or next of kin. Otherwise, let it go.
If “irrational” is code for “religious,” then you should really, really avoid the subject with people altogether.
Don’t forget that human brains are not computers, and therefore do not think in strictly rational ways in general. Hence all of us think irrationally from time to time, and I do not exclude myself.
Moved from General Questions to IMHO.
samclem, Moderator
If by definition someone is “irrational”, you cannot reason with them. Under the circumstances, I would decide if I could live with their thinking or philosophy and keep the friendship alive or simply discontinue the relationship.