Wow, this is unexpected! I am also a Noahide. I just learned of this place this week, and I am still going through the Handbook. I'll make my intro in a separate post.
Someone, hang in there. One of the greatest lessons I have learned is from Rebbe Nachman. The lesson is that even though we sin, we still pray to HaShem. Better that (while at least acknowledging the struggle) than to turn away, in order not to be hypocritical. The Rebbe likened an impure prayer to 'chelbenah.'
'Chelbenah' is one of the main ingredients of the holy incense. By itself, it gives off a repulsive odor. Without this ingredient, however, the holy incense will not acquire its uniquely sweet fragrance, and the mitzvah cannot be fulfilled. So it is with the prayer of a sinner when he prays with the congregation. Even though his prayer is impure, the congregation needs that man's prayer as well. (The full teaching is given at the bottom).
I recall seeing an interview with a Jew, who had lived as a practicing homosexual most of his life. Because he felt he could not overcome his inclination for men, this is one aveirah from which he would not attempt to turn. Therefore, he said it was illogical to observe the b'rit, as long as he would remain stubborn in one particular aveirah.
HaShem does not like hypocrisy, true. Would there not be tears in Heaven, though, over a soul that decided to be "logical" and be wholly evil rather than be "illogical" and at least be partially good?
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From Rebbe Nachman - Sichot HaRan 295
"Encourage yourself to pray. No matter who you are, you can encourage yourself to be stubborn, praying to God. If you are ever discouraged, mediate in the following manner.
I may be far from God because of my many sins. Let it be. If this is so, there can be no perfect prayer without me. The Talmud teaches that every prayer that does not include the sinners of Yisrael is not a true prayer.
Prayer is like an incense offering. However, the Torah requires that incense contain 'chelbenah,' even though chelbenah has a vile odor by itself.
Thus, even if I consider myself a sinner, I am an essential ingredient to every worship service. No prayer can be perfect without me.
I, the sinner, must strengthen myself all the more to pray to God and to trust in His mercy that He will accept my prayer. I am the perfection of the prayer - the chelbenah in the incense.
Just as the vile smelling chelbenah is an essential ingredient of the sweet incense, so my tainted prayer is a vital ingredient of the prayers of all Yisrael. Without my prayer, all worship will be deficient, just like incense without chlebenah."
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As I am learning from the posts I have read, the will to do evil is always awake and very clever. So while this teaching, like many teachings of Rebbe Nachman, encourage us with hope in tough situations, it is not license to sin. The point is never to turn away from our Father in Heaven.