Ulli,
From Jewish perspective there is no need for non-Jews to perform any commands except the seven Noachide laws {and their sub-laws}... Judaism doesn't require the whole world to perform all 613 mitzvot, they are intended for the Children of Israel {The Jewish people} alone as a special covenant between Hashem and us. He loves the entire world and created it all with his everlasting mercy. He desires all creatures to praise him, to love him, and to obey him. Hashem allows evil to exist in the world because it provides the darkness which allows the light of the righteous to shine. We learn that a small candle can bring light to the entire room {ie a small light fills a great space}...
Yom Kippur is a time when the Jewish people have a chance to ask our father in heaven to re-think his judgement which was written on Rosh Hashanah {last week}. This is our chance for repentance. The Jews don't have anything like the Christian idea of confession. I believe Christians have the ritual of confession where they can confess sins whenever they want to. We Jews have a yearly confession, made directly to the Master of the Universe himself. We don't confess to mortal man... We ask for forgiveness from those men and women we offended, we give forgiveness to those who have wrong us. We cry from the depth of our souls for Hashem to show mercy despite the fact that we truly don't deserve what we ask for. We fall far short of our expectations and our potential. We are weak in our ability to resist temptations. We must rely on Hashems mercy because without it our world is doomed.
If a non-Jew can understand what is at stake here then maybe he can move towards the goal of getting close to Hashem. This is the definition of the word Teshuva, which is often translated as REPENTENCE. Actually teshuva is a way to return to Hashem. We all can achieve this, all of humanity. King Davids psalms talk of a day which will come when all the world will know Hashem, praise him, and give their entire being to be close to him... May this day come soon!