Correct me if I'm wrong, but I believe I heard, regarding women and righteous converts, that based on mi'Kerev Achecha Tasim Alecha Melech.
That they cannot attain Comunal Authoritative positions such as Marah DeAsrah, and Shochet.
How were Shmayah and Avtalyon able to be the Nasi and Av Beis Din, or attain Smicha?
Avrahom , United States
While it is unclear from the Gemara whether Shemayah v'Avtalyon were Gerim or descendents of Gerim, the Rambam says that they themselves were Gerim and lists them as the heads of the Sanhedrin in the introduction to the Mishnah Torah. Most probably Shemayah was the Nasi and Avtalyon was the Segan Nasi. This seems contradicted by what you refer to, namely that in the first Perek of Hilchos Melachim the Rambam says that a Ger may not hold a position of authority.
Rav Moshe Soloveichik (the son of ha'Grach, Rav Chayim) resolved this contradiction by saying that the Din that a Ger may not hold a position of authority applies only to an administrative or political apppointment, but not to a position of Torah authority. The only criteria for a Torah appointment are Torah knowledge and Yir'as Shamayim. (See the Ramban to Shemos 23:27 who says that the term "Nasi" applies to both the king and to the head of the Sanhedrin, respectively the chief political authority and the chief Torah authority.)
The problem that a Ger is not qualified to judge is a separate discussion.
Avraham Phillips