Refereeing a fight between happiness and rationality is definitely above my pay grade 😉
However, your sub-question, “If I know that someone is getting full satisfaction (happiness) of a set of beliefs that I know with certainty are irrational, should I try to to talk this person out of his or her beliefs?”, seems like a more practical question to try to answer.
First it is important to distinguish different kinds of “irrational” belief systems.
If by “irrational” you mean:
“Even if you accept their fundamental beliefs (their axioms) at face value their thought process and conclusions are logically faulty, internally inconsistent or self-contradictory”
Than I think you should actively encourage this person to question their existing conclusions and try to make the connections between axioms and conclusions/actions more rational.
“You have a different set of fundamental beliefs than they do and you believe in your heart that your fundamental beliefs are more ‘rational’ than theirs”
Than I am much more skeptical that you should try and talk them out of their fundamental beliefs.
Even uber-rational atheist have some fundamental beliefs that they just accept on faith. No one has a totally rational belief system all the way down to their most basic starting point.
It is hard to me to say that one person’s set of axioms is “better” than another’s.
However, I do think you should encourage others to only accept on faith a small set of core beliefs and that everything else they believe should be based on a rational and internally consistent thought process.
For example, if I met someone whose fundamental belief is “rugged individualism is good” and whose thought process is “smaller government encourages rugged individualism, more Republicans than Democrats have a stated preference for small government, therefore I should support all policies supported by a majority of Republican congressman.”
I would probably not try to change their mind that “rugged individualism is good”, but I would certainly try to change their conclusion that they should “support all policies supported by a majority of Republican congressman”. As I see some logical gaps between the axiom and the conclusion.
If you don’t like that example consider someone whose fundamental belief is “we should do what we can to benefit the poor” and whose thought process is “Democrats talk more about helping the poor than Republicans, therefore Democrats must understand better what benefits the poor, therefore I should support all policies supported by a majority of Democratic congressmen”
Again I would not try to change their mind about “we should do what we can to benefit the poor”. However, I would certainly encourage them to rethink the process that got them to the conclusion that they “should support all policies supported by a majority of Democratic congressmen”. For example, I might encourage them to think again about what it means to “benefit the poor”, to think about the Chinese proverb “give a man a fish and he eats for a day, teach a man to fish and he eats for a lifetime”, etc.
Or think about someone who has a fundamental belief in God, a belief which comforts them and makes them happy. I would not try to talk them out of that belief regardless of whether I personally thought belief in God was rational or irrational. However, if they used an irrational process to go from that axiom to some faulty conclusions I would certainly point it out. For example I would point out that even though the preacher on the radio also professes his love of God that does not mean you should follow all of his advice or that you should blindly accept what he says as true.