It is said that Beis Avtinas were censured because they would not reveal the secret of how to identify the maaleh ashkan. However, the Beis Garmu also would not teach to others the secret of making lechem hapanim. Why then was the Beis Avtinas censured and the Beis Garmu not censured?

In the mishnah Yoma 3:11, Beit Garmu don't come away sounding so good.
ואלו לגנאי: בית גרמו, לא רצו ללמד על מעשה לחם הפנים

(sorry about the late post)
Later on, doesn't one of them give out to secret to somebody, who then realized that they didn't give away the secret leshem shamaim? (because they were afraid it would get into the wrong hands)

You mean when one of the beit Avtinas people gave the recipe to R. Yochanan ben Nuri in Yoma 38a?

Hm... yes. I assumed it was Bet Garmu because they "weren't" censored...
Maybe it was directly related... they're censored, which in turn makes them lose power and wealth, and thereby lose shidduch opportunities. Then the start dying out, then they have no choice left. Just an idea.

(oh. Censored... not cursed... maybe n/m then...)