Of course that’s the case. But, when people in this thread postulate that the rule is “works are paramount, not belief, that’s why atheists can be considered religious Jews” and I show that the “works are paramount, not belief” should lead to the acceptance of people who believe in other gods, as long as they fulfill the works part of the Jewish religion, and then people say, “well, we make the rules”, all I can deduce logically is that “works are paramount, not belief” is not the rule you have in place.
The rule you have in place is more like “you either believe in God or are an atheist, and you do the works”.
So belief does play a role, which is why all the hand-wringing that “NONE, not one, of the 613 commandments in Judaism requires affirming that G-d exists or requires Jews to believe in anything” is clearly false (in terms of explaining who can be accepted as a religious Jew)
Yes, you (the general you) of course can make up your own rules. But when you explain them to others, make sure you explain them accurately and don’t make up rules that you are clearly not using.