What fallacy do you spot in what's written in the photo?

Seems to me that quite apart from the rest of the delusion and incomprehension in that little quip, someone doesn't understand the difference between stochastic and heuristic processes. Just randomly being pitchforked into one state out of many possible, gives you an outcome unlikely before the fact, and implausible after the fact -- a stochastic outcome. In contrast, fine-tuning is radically different in that it can progress indefinitely from even a random start, and even in multiple directions at once, each step being an improvement on the previous. A heuristic process.

Why not read 25 books on the subject? And write 80 pages? It worked for Kushner... 😁

This is a great example of someone who has a cursory knowledge of reason and critical thinking, but lacks either the knowledge or is blocked by ideology to extend this reasoning to the actual logical conclusion.

On the surface, Capturing Christianity appears to be pointing our a solid contradiction in atheist argumentation (ignoring the any possible strawman and "God Is Not Dead" asshole-athiest portrayal). Assuming it is extremely unlikely that a person happens to be born in the correct religion, and it is extremely unlikely that the all the conditions for life are met, then dismissing one because of its improbability and accepting the other does seem hypocritical... as long as you don't think too much about it.

The actual (or steelman) atheist argument: The odds of you being born into the "right" religion, given the number of gods believed in throughout history and in different cultures should make you question that your firm belief in your religion is a result of your culture rather than knowing some unknowable "truths."

The actual (or steelman) Christian argument: The odds that universe could sustain life is unimaginably small, therefore, it is more likely that a supernatural being (God) created the universe. (the strawman version would conclude "therefore God did it").

Regarding being born into the "right" religion, we have numbers on this, at least approximate. We know roughly how many gods were believed to exist in cultures around the world in all times. In other words, we know the alternatives and the odds for the alternatives. With the "fine-tuned universe," the alternative to being the lucky ones who happen to be living in such a universe is... "god did it," which of course, the odds of such a god creating a universe is unknown and unknowable (for all practical purposes). The Christian is implying that they know the odds/probability of the existence of a God who can create universes by magic. This is an extremely unreasonable position to hold.

So yes, it is easy to make a caricature of the arguments/responses and make the atheist look like a fool. But isn't this precisely what Twitter is for? :)

Straw man and Red Herrings. There are no arguments here only exaggerated and hyperbolized interpolations of entirely logical arguments.

I don't see logical fallacies. I don't understand the second statement, it would need context. The first question seems to be a retort to the claim by Christians that the Christian God is the only valid God and Jesus is the only valid prophet, i.e., other religions are invalid. It makes the assumption that if you are born into a Christian family, you will be inoculated to the degree that you will end up Christian yourself. This is mostly true, but not certain. The retort is perhaps exaggerated, but doesn't seem fallacious to me.