Most people can't be swayed through reason on most issues, but many can on some issues, so efficient heuristics to filter out irrationality are invaluable. One red flag is rejecting the below propositions. I summarily refuse to argue with anyone who rejects one of these.
Some things are better than others.
If you don't think some games are better than others, don't argue about game design.
If you don't think some stories are better than others, don't argue about storytelling.
If you are an egoist or moral nihilist, don't argue about morality.
You would think people who claim there is no such thing as objective quality in a given domain would not give any other response to an argument that one thing is better than another, but I've seen each of the above plenty of times. This suggests (if we didn't already know) that the claim is usually insincere; people fall back on it when they don't have any arguments but still want to "win".
A hypothetical doesn't have to be realistic, only coherent, to require an analysis consistent with your analysis of other situations.
This pops up often when I argue with communists: to show them the validity of property, I have to remove complicating factors in the real world to prevent endless red herrings. But many of them complain that my simplified scenarios are "unrealistic" and refuse to consider them.
The most famous proponent of an idea, especially if they died hundreds of years ago, does not have the exclusive right to decide what a word means.
For example, Murray Rothbard's claim that ancaps are not anarchists does not means ancaps are not anarchists.
What Samuel Edward Konkin thought has no direct impact on what we should consider the word "agorism" to mean.
Practicality doesn't affect justifiability.
This is an appeal to consequences. Earnest people can make this mistake, but people who, having it to pointed out to them, insist that the principle is correct cannot be reasoned with.
There is a difference between an initial offense and a retaliation.
You don't have to think retaliation is justified to distinguish it from initial offense.
There is a difference between a group of which most members are X and a group defined by X.
Police are a group defined by their choice to serve an unjust regime. White people are not a group defined by racism, so now matter how many white people are racist, generalizations about white people are not justified in the same way as ones about police.
Often when I criticize my fellow libertarians and anarchists for rhetoric that harms the reputation of our movement, they respond with something to the effect of "FREE SPEECH means you shouldn't even criticize my speech".
And yes, this applies to jokes too. Just because it's a joke doesn't mean it's not a bad thing to say.
Withdrawing from an argument doesn't mean you lost.
A favorite of those in bad faith is to claim that you couldn't counter their argument when you give up on arguing with them. There's nothing you can do to stop this because these arguments are literally endless until you withdraw or a circumstance forces the conversation to end. The only counterplay is to cut such bad faith arguers out of our lives and communities.
Unfortunately, being unable to counter an argument is a very common reason for not responding to it, and there's no non-circular way to distinguish this from not responding because the opponent is in bad faith (or you just don't have time).