Supposedly, but I assume you have to be familiar with baking with applesauce, and not just read somewhere that apple sauce can replace "oil, butter, or eggs" and just shoot for the moon.
It can work pretty well, usually in baked good that have a high moisture content like banana bread. It is certainly not a 1/1 substitute. Best practice is to follow a known recipe, or have played around enough to know what changing fat, sugar, water, levels will do. Just changing something like sugar level will change not just sweetness, but gluten formation, browning, moisture retention. It can be complex.
This is probably sarcastic, but in case it's not: Applesauce is a vegan substitute for eggs, not oil. There is no substitute for oil as many oils are already vegan. You can definitely substitute animal-based fats like butter and lard for others like coconut oil to make a recipe vegan.
It was sarcastic/joking, but wow I had no idea! They seem so dissimilar, I never would've thought that would work. Didn't think I'd learn this much about baking today lol, thanks!
Now, you're going to just brag around with that knowledge of yours, and teach everyone how to write things so that things are correctly understood by the reader?
The OP graphic says "I followed the recipie exactly", which they did not, so somehow I doubt that "facts" matter to them, who are making hyperbolic claims for emotional appeals rather than descriptive purposes.