Is there a logical fallacy for applying fallacies to everything?
This answer is explained more in depth below:
(1) The misapplication of a fallacy is an error and not called a fallacy.
(2) It is always incorrect to apply a fallacy to a valid argument, thus fallacies cannot be correctly applied to everything.
The catch-all fallacy is non-sequitur:
In philosophy, a formal fallacy, deductive fallacy, logical fallacy or non sequitur (Latin for "it does not follow") is a pattern of reasoning rendered invalid by a flaw in its logical structure that can neatly be expressed in a standard logic system, for example propositional logic. It is defined as a deductive argument that is invalid.
The non-sequitur fallacy is really just another way of saying that an argument is invalid:
A deductive argument is said to be valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false. Otherwise, a deductive argument is said to be invalid.
If it is impossible for the premises to be true and the conclusion to be false, then no fallacy has occurred, otherwise some fallacy has occurred. It is an error to say that valid reasoning has a fallacy, so it is an error to apply fallacies to everything.