Tikkun Olam is one of the main missions of a Jew. This is a truth of Judaism. Hashem has tasked the Jewish people with 'Fixing the World'...
I do not associate Tikkun Olam with leftist causes. To do this would be a grave mistake. Every Jew, regardless of their political leanings, is responsible for fixing the world. Fixing the world does not mean making the world like we want it to be. Fixing the world means repairing the damage done to the world through the sins of our prior generations, to fix the sin of Adam and Chava, to fix the sin of the Golden Calf, to fix the sin of the spies, etc...
It is sad that the left has used this term to mean that one should do what he/she 'thinks' is correct. This leads to many non-Jewish causes being called tikkun olam {like helping the enemy, supporting homosexual causes, etc.}.
The Orthodox concept of 'Tikkun Olam':
http://www.ou.org/public/Publib/tikkun.htm
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Our task is to become a particular living example of a set of universal truths, and therefore the conflict between the universal and the particular in Judaism is not a conflict at all because it is only by being Orthodox Jews that we are able to mitaken ha’olam - it is only by being true to ourselves that we can be true to other people. Only if we preserve the sanctity of Jewish family can we talk with authority about the sanctity of the family to the world. Only by studying Torah can we speak compellingly about the value of education and human dignity. Only by having the courage to be different can we be role models to the dignity of difference. That is why Tikkun Olam in my view is the special responsibility of we who are the guardians of Torah.
Maimonides says that when it comes to violating shabbat in order to save a life you don’t do it by employing non-Jews, children, or slaves but it must be the great sages of Israel and the role models who must violate shabbat in order to save a life.[29] Why? Maimonides states that in saving a life you are teaching the most fundamental Torah of all, which is that the judgments and laws of the Torah are not vengance against the world, but compassion, kindness and peace in the world.[30] That has to be done by the role models of Jewish life.
Friends, there are great things left to do. Things we never had the opportunity to do. We have the chance today of shaping a society built on justice and compassion in the State of Israel. We have the chance to be an outstandingly authoritative voice in the moral conversations of mankind. If we do it the world will be a better place; if we do it, we will be better Jews. Why do we say in the festival prayers “you chose us from all other nations, you loved us, you showed us favor?” Because G-d was only interested in us? We say it in order to go on to say “so that one day everything that lives, every human being will acknowledge Him.” How will history judge us if we had the opportunity and like Jonah, in the face of Ninveh, ran away, and we thought only of ourselves? We will not do that. We have to have the courage to engage. That is not only a task for the greatest leaders, it is a task for everyone of us, a task for you and for me. Because every single one of us, by the integrity with which we conduct our business or professional lives, by the grace that we bring to our relationship, by the beauty that radiates from our homes, by the way we use words to heal and not to harm, everyone of us, day by day, is sanctifying the name of G-d in the world.
I repeat there is no formula, no Shulkhan Arukh, and no responsum governing how to be mitaken ha’olam. For this the Orthodox community needs not only masters of the law but also ba’alai nivuah - people with historical insight; that is the challenge of our time. We have thank G-d done magnificently on the two great challenges of Jewish history: Israel and Jewish children. Now what stands before us is the third great, untouched challenge of tikkun olam that we, in a secular age, should become role models for spirituality. That we in a relativistic age should be able to teach people once again to hear the objective “Thou shalt” and “Thou shalt not”. In an age in which religion so often brings conflict we should teach once again that Shalom, peace, is the name of G-d and that the mighty is one who turns an enemy into a friend. If we do these things there will surely come to all of us that experience of living a Jewish life and knowing that those around us, those with whom we have dealings are blessed by that life, and they will return to us saying: you have been a prince or princess of G-d in our midst. Do that and we begin to perfect the world.