Mitzvot only apply to bnai brit peoples
Mitzvot have applicability to only bnai brit peoples. A brit requires an oath. No oath No brit simple as pie. Man received the name Adam because he was formed from the earth. When "Adam" eat from the tree of knowledge this resulted in the divorce of the human soul from the earth. Consequently the Creator cursed the land. The brit relationship repairs this damage. Consequently the Creator swore to give certain lands to the bnai brit peoples.
Doing mitzvot operates on 2 levels:
(1) the reward results in a re unification of the Neshamah to the promised land, hence the Talmud teaches that if a person dies abroad that his/her neshama has to roll back to the promised lands interesting metaphor!
(2) the performance of mitzvot by the bnai brit peoples acquires heaven and earth, establishing our brit Elohim to be specifically Ehohi of the promised lands.
Obviously the other lands of the earth, non bnai brit lands might and do have other gods. But this falls outside of the parameters of the bnai brit peoples b/c by our oath/brit we swear only to seek and obey our brit Elohim. For a bnai brit to worship other gods this profanation of the oath/brit thereby results in false and futile vanity, this understands the metaphor employed by the prophets when they described idols made of wood and stone.
The logical inference takes the specific and applies it to the general; meaning that just as its silly to bow down and worship gods of wood and stone its silly for the bnai brit peoples to worship any of the other gods irregardless if they are wood or stone or allah or jesus or Buddha etc etc etc. this all comes into the category of avodah zarah. Now it should be clear why idolatry is a very bad translation of avodah zarah.
To date to my knowledge no bn candidates have sworn or cut an oath/brit. No bn candidates have dedicated or affixed their neshamot to live in a particular paradise. Until these basis requirements are achieved, it seems to me that bn candidates accomplish nothing by doing commandments who's relevance only touches bnai brit peoples.