Change the Uncomfortable Subject

Some characters feel a current line of discussion is really inappropriate, and they make it clear they should move on to something else. Sometimes they say "moving on", or just leap into another topic.

Reasons the current subject isn't working can vary. Either it's Squick, Too Soon, or even something like a Metaphorgotten line.

There's a hand gesture that shows up frequently in Anime and Manga, that means basically this.

Compare Stunned Silence, Shutting Up Now.

Contrast Digging Yourself Deeper (trying to talk your way out of an uncomfortable subject, and utterly failing).

Examples of Change the Uncomfortable Subject include:

Anime and Manga

In Saint Beast, Luca is the main instigator of this, knowing that relating mutinous sentiments is very dangerous under the tyrannical rule of Zeus. Pandora also tries to guide Judas away from defiance at the end of the prequel series, but Judas indicates that he's done silencing himself and intends to openly defy Zeus' rule.

Film

The Emperors New Groove: In the opening, Kuzco asks for a flashback to where the story began, but the flashback goes back too far:

"See, this is a little too far back. Ooh, look at me! That's me as a baby! OK, moving on."

Live Action Television

Frasier Crane does this a lot.
In the Doctor Who serial The Ice Warriors:

Jamie: You see how those lassies were dressed?
Victoria: Yes, I did. And trust you to think of something like that.
Jamie: What? Couldn't help thinking about it.
Victoria: Well, I think it's disgusting, wearing that kind of thing.
Jamie: [Mocking] Oh, aye, so it is, so it is. You er, you don't see yourself dressed like that then?
Victoria: Jamie!
Jamie: Oh, I'm sorry; it was just an idea.
Victoria: We will now change the subject, please.

On Seinfeld, George and Jerry do not like it when someone does this; they prefer to let conversations continue until they reach a natural end. There's a reason this show's the Trope Namer for Seinfeldian Conversation.
In The Vicar of Dibley, David constantly does this when the council meetings go off topic. "Moving on..."
Chandler in Friends did this when other people had raised the subject. "The word you're looking for is 'Anyway...'"
Happened a couple of times in Criminal Minds
- While the team was eating in a Chinese restraunt in "A Real Rain", they were talking about the case and then Elle asks to change the subject. Hotch asks if she's seeing anyone and then Elle begs for them to talk about the case again.
- A case of Right Behind Me in "The Bittersweet Science".

Garcia: (via webcam) Okay, Rossi, out with it. Is Hotch dating anyone?
Rossi: (leans in to the webcam) I. Don't. Know
Reid: You know, statistically, widowed men start dating much faster than females, but Hotch is refuting the data. It's been two years and 19 days.
Garcia: Venus has aligned with Mars, which means love is in the air and maybe we will have weekends off.
Morgan: (sees Hotch and clears throat to warn Garcia)
Garcia: What? Is he standing there? He's standing there, isn't he?
Hotch: Hello, Garcia.
Garcia: Hello. Someone talk about the case.

Web Original

In Sailor Moon Abridged, Serena called Raye "emo", and everyone else Gasped, likely because that was a running joke about Sasuka in Naruto the Abridged Series. Then Luna said this line.
Linkara of Atop the Fourth Wall said this after his horrified expression of seeing a comic start with the top of the World Trade Center blown off.
Done in this review by Classic Game Room of Art of Fighting 3, when the reviewer lost his train of thought.
In Captain SNES, Relm and Celes do this after Terra mentions that she saw her parents conceiving her in a vicarious flashback.