It could be, but it doesn't have to be. It all depends on the characters involved.

The DM can referee in the dispute but they (usually) can't say your character would or wouldn't believe something.

A good DM might ask you to in-character justify your bias, for example. They're also supposed to listen if you say "I don't trust Count Fuckface on account of him having a history of being a Fuckface and also he's standing over a cooling corpse with bloody hands."

If a player is metagaming that's a separate problem from their character being biased, or having a reasonably justified suspicion or whatever.

Or never, ever being interested in the creepy player's character because they don't like their vibes.

Every edition since at least 3.0.

In the sections describing how skills work and what circumstances you should allow checks for them, and the sections describing bonuses to those checks, what the role of the DMs and players are, including several very specific references to how character attitudes are very important to the DCs of those checks and the fact that skills only affect those attitudes in the first place and they aren't mind control.

In other words, the whole fucking thing.

Sure, you can agree to anything.

If you didn't think it through and thus suffer from skill issues.

And there are of course good stories to tell with it, like in this secret traitor situation, and good players will apply circumstantial bonuses fairly.

Like perhaps that paladin doesn't WANT to believe their comrade is a murderer.

Doesn't mean you shouldn't be aware that another player can't force you into simple contested rolls on the nature of reality that you can't possibly contest, ever.

Hell, even if they're right! You can play a completely deluded madman that looks at a windmill, hears an NPC tell him the absolute, objective truth that it is a windmill, and decides it's a giant instead.