I can not think of any another good phrase to describe the sense, "Open Hearted". This characteristic is like one who does not posses the nature of being stubborn, who has the ability to listen and in certain cases accept others' theories though they can be in opposite of his own theory. A good example would be if a person is capable of admitting if there is some bad customs in his own religion and he does not fall back to admit it in front of others and change the custom in his regular life. What is the name of this characteristic?
The phrase you're looking for is actually "open-minded". When one is open-minded, they're willing to listen to other opinions and, if properly convinced, change their beliefs. The opposite of this would be closed-minded, like when you enter into a discussion with someone and they refuse to hear anything you have to say or change their mind.
"Open-hearted" would be more like someone who is very generous and caring, and is always there to give a helping hand.
Definitions for each:
- kindly and warm
- disclosing intentions and thoughts clearly; candid
Receptive to new and different ideas or the opinions of others. See Synonyms at broad-minded.
Other ways to say this would be "easy going" or "flexible".
Joe is such an easy going guy. He never argues with Bob, even when everyone knows that Joe is correct.
Jane is pretty flexible – she never gets hung up on the sticky parts; instead, she focuses on the big picture and getting things done.
NOAD defines easy-going as:
relaxed and tolerant in approach or manner
and lists tolerant and broad-minded as synonyms. This may not be completely synonymous with open minded, but there is some overlap. Similarly, NOAD defines flexible as:
(of a person) ready and able to change so as to adapt to different circumstances
Here, "different circumstances" can be applied much more broadly than matters of beliefs and opinions (such as coping with an unexpected job change). Still, the word might be used when talking about the situation you described.
...does not posses the nature of being stubborn, who has the ability to listen and in certain cases accept others' theories though they are opposite of their own theory. A good example would be if a person is capable of admitting if there is some bad customs in their own religion and he does not fall back to admit it in front of others and change the custom in his regular life.
I know that this is not as obvious, but I think the best choice is "reasonable," which means "able to reason" and carries with it the implication that someone is able to put aside his personal differences and analyze things fairly, as they are (i.e., to reason). "Open-minded" is not bad, but it implies only an openness to receiving new ideas, not the ability that you described (not stubborn, able to listen, and willing to accept the better theory) which is reasoning.
The adjective is "reasonable" and the noun is "reasonableness" or "reasonability."
I admire how Joe, a Democrat, voted for the bill he agreed with, even though it was written by a Republican. Joe is a reasonable guy.