Economics has a number of definitions, and in the context of using a verb like "adhere" it makes more sense to assume one refers to a definition along the lines of "economic conditions," a definition also easily available with a quick Google search. Your use of the adjective "American" further reinforces this reading, since "American economics" is not a uniform branch of economics as a social science, while "American economics" with "economics" defined as "economic conditions" is something that can actually be defined and makes sense (the economic conditions of the US).
I have not backtracked at all, I used common definitions of each word and simply replaced them in my sentences. You’re the one backtracking.
You really never know when to concede. Yes, economics has multiple definitions. Of which, all conventional and frequent uses pertain to it as a study, or science. Just to be clear, since you're often throwing around words around carelessly - "Science" is a study as well, obviously a more refined study with select guidelines/rules in which we observe such, but nonetheless it is definitely a study. I can adhere to the science of animal breeding, without breeding with animals. I don’t need to replace “economics” with “economic conditions” to infer that I am talking about the STUDY of the system.
Also, you’re trying to claim when it is and isn't practical/common place to use the word adhere. Sorry, but I can say "I don't adhere to the study of...." or "I don't adhere to the science of..." And it makes plenty of sense. You're really grasping at straws here. And the main confusion you’re mixing up is the practice of the study of an act/event/system/environment and the practice within that act/event/system/environment.
P.S. Just to be clear too: You keep throwing around "American Capitalism" - Capitalism, is the system itself, not the study of the system - the study of such systems is economics. You once again swapped these words like they were nothing (lol).