It's hard to interpret ppl you disagree with charitably, but it's worth a shot, because at least that way you won't be angry on the internet as much.

There are a bunch of ways to interpret the tweet so that it's fine, or at least not sophistry. Let a practice be "rational" if it works towards the ends of the majority of the people involved in the practice. Then, a practice is not rational if the majority of the people involved in the practice have some ends e1, e2, and so on, which the practice isn't serving.

An example of a practice that isn't rational is plausibly the practice of making nuclear weapons during the cold war. The practice threatened the existence of the human race, and therefore a fortiori the ends of those involved in it. Hence the practice is irrational by definition.

Is an exclusively profit-driven enterprise irrational according to this definition? It's plausible that it is. Suppose that an enterprise has the option of outsourcing a factory where a majority of its workers work. Suppose further that it's not bound by economic necessity to do so: while doing so will maximize its profits, it won't go under if keeps its factory at home. If the enterprise is exclusively profit driven, the enterprise will opt to outsource the factory. In doing so, it fails to serve the ends of the workers who work for the enterprise. So, by definition, the enterprise is irrational.

Finally, it's plausible this wouldn't have happened if the enterprise were a worker cooperative. So, we have a clear and plausible case of where the profit motive causes irrationality. Now, I'm not saying that this argument is correct, but it's certainly not sophistry. I'd argue that something like it is what the existential comics guy had in mind when they drafted their tweet.