"Cochinita? No, Faux-chinita." Pibilio Diaz drops the science on roast pork.

yes

I don’t think you could reasonably make a hard rule for something that subjective. Maybe you could draw the line at something fundamentally changing the dish, but then you’d have to argue over what a fundamental change is. Take carbonara (I’m taking a risk with that one), for example. Swapping bacon for guanciale doesn’t fundamentally change the dish, because it only substitutes one ingredient with a very similar and common alternative. Adding mushrooms to a carbonara doesn’t fundamentally change the carbonara; it just adds an ingredient, and it won’t make the rest of the dish unrecognizable. Making carbonara with an eggless cream sauce, on the other hand, changes the sauce that makes carbonara carbonara, and someone familiar with traditional carbonara would probably take it for a different dish. Still, some people would probably disagree with what I think is a fundamental change. Putting too much thought into it would lead to splitting hairs and arguing over whose subjective opinion is right. I think I’ve already put too much thought into it.

However, I do know that if someone says a dish is invalidated from being a specific dish by the addition of a single pinto bean or a sliver of jalapeño on the side at the end, it’s probably gatekeeping.

Also, beef hot dogs with taco fillings as toppings are pretty tasty, even if I wouldn’t personally call them tacos.

When is a dish sufficiently changed to the point that is no loner that dish? Like, Chicago Style Pizza is still Pizza, but is a Hot Dog a Taco?

By quantitative logic you'd define a dish by certain attributes, giving each a certain weight; then you add some arbitrary cutting line saying «if it scores below X, it isn't [dish] anymore». But in practice language doesn't work like this, people in general have some mental prototype on how a dish «should» be and use it in comparison with the dish at hand.

Sometimes when we run out of tortillas we use bread as a substitute. Both basically have the same function even if they're made from different ingredients and by different cultures.

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I mean, completely aside from his phrasing....if you shred it with a fork, it's not cochinita pibil anymore? If you accidentally shred it too fine, it isn't anymore? If it's served with the wrong side dish it isn't cochinita pibil anymore? Those are just ridiculous assertions. This is some carbonara level food gatekeeping that I would be shocked if people in the yucatan it kept to such strict guidelines. Half of his "rules" have nothing to do with the dish itself but rather everything around it. I get that this is a traditional dish from a small area that has been probably cooked the same way for a long time, but taking a food out of it's original context doesn't mean it's something different. I'm really curious what he would call cochinita pibil that is served in the vicinity of beans. Probably some long, convoluted sentence like "pork shoulder cooked in the style of cochinita pibil served with beans".