I think it would be good to separate the analysis into FGCA's which are always fallacious, versus those that are only warning signs/rude. For instance, the fallacy of grey is indeed a fallacy, so using it as a counter-argument is a wrong move regardless of its generality.
However, it may in fact be that your opponent is a very clever arguer or that the evidence they present you has been highly filtered. Conversationally, using these as a counter-argument is considered rude (and rightly so), and the temptation to use them is often a good internal warning sign; however you don't want to drop consideration of them from your mental calculus. For instance, perhaps you should be motivated after the conversation to investigate alternative evidence if you're suspicious that the evidence presented to you was highly filtered.
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.