The cult one can be legitimate if the cult claims to have a source of absolute, no-interpretation-needed, truth and various cult members use it as reason to believe (separately) in P and ~P. While no individual person believes contradictory things, just the fact that the cult's "absolute truth" can be used to deduce two contradictory things is a sign that it isn't very good as a source of absolute truth.
Follow-up to: Knowing About Biases Can Hurt People
See also: Fully General Counterargument (LW Wiki)
With the caveat that the arguer doesn't need to be aware that this is the case. But if (s)he is not aware of that, this seems like the other biases we are prone to. The question is: Is there a tendency or risk to accidentally form FGCAs? Do we fall easily into this mind-trap?
This post tries to (non-exhaustively) list some FGCAs as well as possible countermeasures.
The List
Here is a list of my own making:
Do you now some more? Into what clusters do these FGCAs fall?
Self-sealing Belief
Why do we use FGCAs? One reason may be when we are arguing from within a self-sealing belief:
Preventive Action
What are known ways to avoid FGCAs?
One specific method against this mind trap is being humbly gullible.
Another is to practice Steelmanning as long as you avoid the dangers of steelmanning. Especially applicable is Steelmanning Inefficiency.
More general advice can of course be found in the Twelve Virtues of Rationality. See also the concise and improved versions.