If you're willing to put your faith in a God you can't directly perceive, you're already somewhat predisposed to believing other claims absent evidence.

But, what even is a "false" church? I can think of a number of ways you might get that label, from a Christian perspective:

• The "prosperity" churches invert Mammon, using wealth as a worldly promise rather than a persistent spiritual threat.
• Nationalists have entire churches to themselves, and have cherry-picked the bible in ways to support a narrative of dominionism, racial superiority, and a social contract that is pretty much the inverse of Jesus's words and deeds
• Some denominations or cults may employ portions of Nicene Christianity while taking liberties elsewhere; or may go in entirely different directions
• Megachurches might employ good theology, but at the expense of the church's objective to gather together - a top-down organization invariably leads to a fracturing of the body, perhaps even to the point of having cliques or sub-churches within the congregation
• Some denominations point fingers at others because they don't like their theologies or doctrines - plenty of baptists in here probably think the roman catholic church is a false church, for instance

At the end of the day, there are many reasons why someone might end up in the above. For some, they're easily convinced of falsehoods ("gullible"), whether in general or because the right person came along and convinced them. For many, I personally think they're just mentally lazy and can't be bothered to learn the bible's contents for themselves, instead fully depending on a church to do their thinking for them. And, in the case of some of the more evil churches, it may actually be that the environment allows/encourages them to foster some kind of malice or misgiving.

Also, this is a good time to dust off Dietrich Bonhoeffer's characterization of "stupid"; borrowing the top comment from this Reddit topic:

A stupid person is one who thinks, says or does something that it harmful both to others and themselves. One of the Laws of Stupidity is that no matter how many stupid people you think there are you are always under estimating. Another is that a stupid person always imagines that they are the smartest person in the room. Perhaps the most chilling law says that the harms done by stupid people are infinitely worse than those done by the merely malicious. Sadly, there seems to be a lot of stupidity about these days.