It's simply that 大根 (daikon) is literally just a type of white turnip, and there is slang usage of it as "大根役者" (daikon yakusha), which would be more literally "daikon actor", meaning someone is a bad/hammy/too stiff of an actor.

Emunenekasa look at Nagamine's acting, and think he kinda sucks, so they made a visual gag of showing daikons behind them as they hold their tongues to show what they are thinking/audience can get what they were going to say, as to my knowledge it's a common enough visual gag when you make fun of someone's acting in media (and Emu even starts to say that phrase before she's shushed, because Nagamine's fans are around, so let's not get jumped and cause a scene today)