I\'m trying to explain to my team why this is bad practice, and am looking for an anti-pattern reference to help in my explanation. This is a very large enterprise app, so here
IMO the fundamental design principle at play here is encapsulation. In your proposed solution you have encapsulated the logic inside of the Thing class, where as in the original code the logic leaks out into the callers.
It also violates the Open-Closed principle, since if you want to add new subclasses that support X you now need to go and modify anywhere that contains that hard-coded list. With your solution you just add the new class, override the method and you're done.