Why Gandalf silenced the hobbits in front of the voice of Sauron?

[badlands]

So they won’t have him make fun of them?

[Alvin Eriol]

I assume you meant the "Mouth of Sauron".

Hobbits, plural? Only one, Pippin, was present before the Black Gate during the parley.

Gandalf shushed him because he, by his outburst on seeing the mithril hauberk, was giving away intel to the Mouth, i.e. the Mouth now knew Pippin recognized it. That raised the possibility Sauron might surmise Mordor had been infiltrated, and would order a general alarm and search, the very thing Aragorn and Gandalf had tried to avert. However, it was still unlikely such an intruder would be the one having the Ring, and what could one spy or guerilla possibly do otherwise? It worked out to be another distraction for Sauron and his inner circle, much as the orcs' fight at Cirith Ungol Tower over the mail-shirt made it possible for Frodo and Sam to get into Mordor to begin with.

[Michael]

I don't disagree with anything you said, Alvin, but I think the scene follows a familiar trope in fiction: never show weakness to an enemy. Many a story has a moment where a character is prompted into revealing some emotion to an enemy in much the same way. The bad guys bring out clothing or artifacts that belong to another character who has supposedly been captured or killed.

I can't be sure but I think this trope predates Tolkien.

See the "Our Hero Is Dead" trope at TVTropes:

https://tvtropes.org/pmwiki/pmwiki.php/M...HeroIsDead