(Mishnah): An Arel is Mechalel Avodah.

Ta'anis 26b (R. Yehoshua ben Levi): Parshas Nazir is next to Birkas Kohanim, to forbid a Kohen who will Duchan to drink wine, just like a Nazir.

Question (R. Zeira's father): If so, one who ate Chartzan (grape peels) should be forbidden to Duchan!

(R. Yitzchak): "Lesharso u'Levarech bi'Shmo" - just like Sherus (Avodah) is permitted after one ate Chartzan, also Berachah.

Suggestion: Just like a Ba'al Mum cannot serve, he cannot Duchan!

Rejection: The Hekesh to Nazir shows that he may. These Hekeshim are mid'Rabanan, so we are lenient.

Rambam (Hilchos Tefilah 15:3): If a Kohen murdered, even if he did Teshuvah, he does not Duchan. If he served idolatry, whether b'Ones or Shogeg, even if he repented, he never Duchans. Other Aveiros do not disqualify.

Rambam (6): If a Kohen did not have one of these disqualifications that inhibits Birkas Kohanim, even if he is not a Chacham and is not meticulous about Mitzvos, or everyone murmurs about him, or his business dealings were not just, he gives Birkas Kohanim and we do not stop him. This is a Mitzvas Aseh for every Kohen qualified for Birkas Kohanim. We do not tell a Rasha to be a bigger Rasha and refrain from Mitzvos.

Shulchan Aruch (OC 128:37): A Mumar to idolatry does not Duchan. Some say that if he repented, he Duchans (Rema - this is primary). If he was forced, all agree that he Duchans.

Mishnah Berurah (134): We learn from Avodah; he is Pasul for Avodah. A Mumar to be Mechalel Shabbos in public is like a Nochri, and he does not Duchan.

Kaf ha'Chayim (217): A Mechalel Shabbos is Pasul to Duchan only if he transgressed mid'Oraisa, and in front of 10 people.

Tzitz Eliezer (13:14): In Likutim Halachos, the Chafetz Chayim was in Safek whether a Mechalel Shabbos in public is a Ben Nechar who is Mechalel Avodah, since he is like a Nochri in every way. Seemingly, we can resolve this from what he himself wrote in Mishnah Berurah (134), that a Mumar to be Mechalel Shabbos in public is like a Nochri, and he does not Duchan. We learn the Isur to Duchan from Chilul Avodah. We are much more lenient about Birkas Kohanim. If so, since one who is Mechalel Shabbos in public may not Duchan, all the more so he is Mechalel Avodah. The Pri Chodosh, Pri Megadim and the Aderes (at the end of Orchos Chayim) say that it is obvious that one who is Mechalel Shabbos may not Duchan. We should be stringent like them until the Kohen repents. If there are different opinions in the Beis ha'Keneses and not all will heed the Rav and strife will result, one should do like Rav Levitan says, and be silent. If they go to Duchan by themselves, he does not tell them to descend. There must be at least one Kosher Kohen at the Duchan with the Mechalelei Shabbos. If there is concern that if they do not come to Duchan in the Beis ha'Keneses on Yomim Nora'im and festivals, they and their children will forget that they are Kohanim, and they will become Tamei Mes and marry divorcees (which they avoided until now), one can permit them to Duchan and rely on reasons to be lenient in time of need.

Bach (23): If one's brothers died due to Bris Milah, and therefore, he is an Arel (uncircumcised), he is Pasul for Avodah. A Hekesh equates Birkas Kohanim to Avodah. Why didn't the Poskim say that he is Pasul for Birkas Kohanim? Perhaps this is because in Sanhedrin (83b), we say that an Arel is not Chayav Misah for Avodah. He transgressed only a Lav. Anyone who is exempt for entering the Mikdash may Duchan, like I explained about one who drank. This requires investigation.

Magen Avraham (54): We say in Ta'anis that the Hekesh is only to be lenient, to permit Chartzan, but not to be stringent. A Ba'al Mum and many others Pasul for Avodah taught in the second Perek of Zevachim are Kosher for Birkas Kohanim. Semag (Mitzvah 20) says that a Mumar is Kosher for Birkas Kohanim. The Hekesh is only for standing. Even the Rambam and those with him, who disqualify a Mumar, say that this is a fine regarding Avodah, and similarly for Birkas Kohanim. Where there is no fine, they agree that he can Duchan. The Rambam says that one who is drunk is Pasul due to the Hekesh of Berachah to Avodah, to teach that just like if he paused while drinking or mixed in any water he is exempt, the same applies to Birkas Kohanim. Had we learned from Nazir, we would have forbidden one who drank any amount, even if it was diluted. Even if he did not circumcise himself b'Mezid, he is Kosher, like the Rema (Sa'if 39).

Bi'ur Halachah (DH v'Im): The Magen Avraham says that if an Arel's brothers died due to Bris Milah, he gives Birkas Kohanim, even according to the first opinion in this Sa'if, like the Rema says in Sa'if 39. This is from the Rambam, who is the first opinion here. The Bach was unsure whether the Hekesh of Berachah to Avodah disqualifies him according to the Rambam. The Chemed Moshe, Eliyahu Rabah and Pri Chodosh explain the Rambam like the Bach. Eliyahu Rabah connotes that even the second opinion, which does not make the Hekesh, disqualifies an Arel. Perhaps this is like one who sits (while blessing) or marries forbidden women, which all disqualify. I say that if the Arel did not circumcise due to Ones, i.e. his brothers died due to Milah, surely we can be lenient, for we allow a Mumar to idolatry who repented to Duchan, for we do not make the Hekesh. Or Zaru'a and Shibolei ha'Leket explain that since he did not lose his Kedushah, and a divorcee is forbidden to him, he is also Kadosh for Birkas Kohanim. No one would think to permit an Arel Kohen to marry a divorcee! Pri Chodosh's proof from one who marries forbidden women is invalid. There he transgresses, so we fined him and do not give to him attributes of Kehunah as long as he profanes himself. (Once he divorces her and vows Al Da'as Rabim not to benefit from her, he gets back his Kedushah.) Here, this is total Ones. He is no worse than one who became a Mumar and repented, whom we allow to Duchan. Eliyahu Rabah was stringent, because he cannot eat Kodshim, so he is worse than a Ba'al Mum. This is wrong. A Tamei Kohen cannot eat Kodshim, yet he Duchans, like the Pri Megadim says. R. Tam says that an Arel is Pasul for Avodah only if he does not circumcise b'Mezid. If his brothers died, he is Kosher. Even though many disagree, we can join his opinion for Birkas Kohanim, since most hold that the Hekesh of Berachah to Avodah is only mid'Rabanan. If he did not circumcise b'Mezid, one should be stringent like the Pri Chodosh. He is like one who marries forbidden women.

Kaf ha'Chayim (222): Several say that an Arel does not Duchan. Mishbetzos Zahav (39 DH v'Hinei) says that even if he ascended to Duchan, he goes down.

Shulchan Aruch (39): If there was nothing about a Kohen that disqualifies from Birkas Kohanim, even if he is not meticulous about Mitzvos and everyone murmurs about him, he gives Birkas Kohanim.

Beis Yosef (DH Lo): This is the Perush of the Yerushalmi, which says 'do not say that Ploni transgresses Arayos and spills blood. Will he bless me?!'

Mishnah Berurah (143): This is even if he transgressed severe Aveiros such as Arayos.

Mishnah Berurah (144): This is even if what they say is true, i.e. his evil is public knowledge.

Rema: Other Aveiros do not inhibit Birkas Kohanim.

Magen Avraham (56): Ra'anach (Mayim Amukim 2:42) says that this is if he repented. In any case, we do not disqualify a Kohen due to bad repute.

Gra: This is even if we know about the Aveiros, since we say (Sa'if 35) that if he murdered, he does not Duchan. This is if he did not repent, like it says in Sa'if 35. Even the Rambam agrees to this.

Mishnah Berurah (145): Only idolatry and murder disqualify.

Mishnah Berurah (146): This is even if he did not repent.

Mishbetzos Zahav (39 DH Kol): One who transgresses to anger Hash-m is like a Nochri, so he does not Duchan.

Igros Moshe (OC 2:33:2): Even though the Rema (YD 264:1) says that a Mumar to Orlah is like a Nochri, the Shach (5) says that this is only to disqualify him from circumcising others. For everything else, he is not a Mumar.