Say a convert is called to be one of the three witnesses for a person's conversion. May he do so? The reason why I am asking is that I know there are restrictions on gerim for serving on a beit din, mostly on matters when the person of question being approached by the beit din is a born Yisraeli, so I would like clarification and opinions brought forward arguing for either case.
Thank you DoubleAA for commenting with the relevant essay, I'll just summarize.
To sum up Rabbi Michael Broyde's excellent essay:
R' Shlomo Kluger, R' Akiva Eiger -- no, according to the majority medieval opinion that a convert can't financially judge a born-Jew.
Rav Elyashiv, R' Hershel Schachter -- no, according to all medieval authorities, as a convert can't supervise a chalitza.
R' Gedalya Felder, Bet Mordechai and others -- yes according to all medieval authorities, as it's like judging a non-Jew.
(The Conservative movement allows it outright, and Rabbi Broyde has serious concerns with their logic.)
Rabbi Broyde's personal opinion, working from the above dispute, is that we (generally) shouldn't advise someone to get a conversion that will be invalidated by many significant opinions. Therefore, a convert shouldn't usually serve on a gerut bet din.
If, however, someone did already convert using a panel containing a convert, Rabbi Broyde would rely on the lenient opinions and consider the person Jewish.
There are, unsurprisingly, other Orthodox rabbis who will conclude "totally yes!" or "totally no!", depending on which reading they follow.