The Fallacy of Fallacies
There's a peculiar trend forming in the atheist community that has seemingly romanticized logical fallacies and, accordingly, treats them with affection and reverence. Nonbelievers are familiarizing themselves with commonly used logical fallacies in an effort to go online or out into the world and be able to deliver a philosophic knockout punch when in discussion with religious adherents. It's a subset of a much larger trend which sees a portion of the atheist community actively seeking theological debate with religious people—a peculiar desire, the merits of which can and probably should be addressed elsewhere. Specifically, nonbelievers are engaging in debate and listening to religious arguments like a cat crouched in tall grass, and upon spotting a false equivalence or appeal to ignorance, set their teeth, fill their lungs with air, and leap forward with a battle-cry of, 'Fallacy!' In doing so, however they are generally giving their opponents' arguments far more credit than is deserved and doing a bit of a disservice to their own position in the process. Telling a person they've committed a logical fallacy is admitting they've made a good argument. It's a nice thing to do, and appropriate when deserved, but dizzyingly confusing when not deserved.
If intro-level logic and critical thinking courses represent reality in a reliable way, it's been established that a successful argument must be both sound and valid. A well-constructed argument is sound; an argument whose conclusion follows from that construction is valid. A = B and B = C, therefore A = C. That's a solid argument. You'd have a hard time taking the contrary position. If a philosophical opponent comes at you with A = cottage cheese and kitties are warm, therefore Trump 2016; they've committed a formal fallacy. Their argument is neither sound nor valid. It's a dark mess. No rebuttal is necessary for such an argument. You don't need to take the contrary position—you're dealing with a lunatic and need to get to a safe place. Your best response to a formal fallacy is to find a soft chair from which to sip a strong drink and do your best to reboot your nervous system.
Informal vs. Formal Fallacies
Informal fallacies are where things get sticky. Informal fallacies are the ones atheists like to memorize and spot from high places. When telling someone they've committed an informal fallacy, however, they're admitting their opponent's argument is both sound and valid (A = B and B = C, therefore A = C), but may fall apart due to one or more predefined technicalities—for example, B is an authority figure, therefore an appeal to authority has been made. Religious arguments rarely ever make it this far. They almost always fall apart in construction and sink into the quagmire of formal fallacies. To assign informal fallacies to religious arguments is to give them a smile and a pat on the back they generally don't deserve.
Here's less extreme example of a formal fallacy: 'Sean Hannity says anthropogenic climate change is a myth. I believe everything Sean Hannity says, therefore anthropogenic climate change is a myth.' In this case A is climate change, B is Sean Hannity, and Cis people's whacked-out propensity to listen to the things Sean Hannity says. A large portion of the fallacy-loving atheist community would parry with, 'Appeal to authority!' and ready themselves for the next thrust. That's accurate—in a way—but look at the noisome logical turd that appeal to authority is sitting on. The person making this argument hasn't validly reached the conclusion that anthropogenic climate change isn't real, he's reached the conclusion he's an irretrievable idiot. To call him out on an appeal-to-authority fallacy is to concede he reached the conclusion he was aiming for when he wasn't even halfway close to being halfway close.
Another example in a similar vein: 'Ninety-seven percent of climate scientists have reported findings consistent with anthropogenic climate change. The scientific consensus was arrived at using reliable data, therefore anthropogenic climate change is real.' Again, you might say, 'Ah-ha! Appeal to authority—that's a logical fallacy.' You'd be absolutely right, of course; that is a logical fallacy. You'll also have made a bit of an ass of yourself, because the logic is sound and valid. An informal fallacy won't even dent it.
So that's the bad news. Informal fallacies don't deliver the knee to the crotch as they've been widely reported to do. The good news is the need to invoke an informal logical fallacy is exceedingly rare. If you want to show a person their argument is absurd, simply break it down into its base components and examine them individually. For example, 'Sean Hannity says anthropogenic climate change is a myth.' Yes, but Sean Hannity is a giant moron. He also has a vested financial interest in denying climate change. He also has no formal climate science training and is uniquely unqualified to make claims in either direction. There—A has been taken apart before B was even able to poke its head out. In hacking at the root of the argument before it's completed, you've rendered your opponent's venom inert and have stopped the arrival of a conclusion entirely—and you've done so without having to memorize a list of obscure logical pitfalls.
So that should save you a bit of time.