Obviously, anyone can be fake, but how they go about it is a little different depending on which functions you value.

Fe types fake their emotions, enthusiasm or interest, and Fi types fake their closeness, being your "friend" to get what they want. For whatever the reason, extroverts are more likely to be "fake" than introverts.

IXFxs can also be fake, but supposedly they're the "sincere" types, so they're more likely to emphasize on emotional or relational sincerity.

EXTxs are kind of clueless, so they can fake both, but more pronounced on either Fe or Fi that they value.

IXTs are just hopeless, so they don't even try to be fake. At best, they use some form of emotional manipulation. But ISTxs are slightly better at it than INTxs.

I would not necessarily say that being "fake" is a bad thing. It can be the lubricant that grease the wheel, the glue that holds society together. EXFx types often make people feel good by being "nice to everybody", "everybody's friend", and that's not really a bad thing.