Strictly illegal. By the way, illegal in AL.
Too many references to gods everywhere else in the Players Handbook and other core rules.
Impossible to play without running into gods.
Yet, I was able to play D&D for twenty years with joy. Sadly, 5e changed the game.
*sigh*
Just for the sake of total clarity on the actual & official 5e rules of the game... I am going to quote page #56 of the 5e PHB, under the entry entitled "Creating a Cleric", the last sentence of the very first paragraph states unequivocally: "Check with your DM to learn which deities are in your campaign."
So, upon checking with the DM, hopefully they will have read the actual rules, and can helpfully quote page #10 of the 5e DMG, under the entry entitled "Gods of your World", the very first paragraph states unequivocally: "As far as the games rules are concerned, it doesn't matter if your world has hundreds of deities or a church devoted to a single god. In rules terms, clerics choose domains, not deities..."
Regarding the AL, the so-called deities of the Forgotten Realms are simply intermediaries for imbuing clerics with spells. The cleric is required to choose a "deity", it does not articulate any requirements regarding the character's relationship to that entity, nor does it even require the cleric to actually worship the "deity"... The cleric could be a devout Christian, Muslim, Hindu, Jew, Buddhist, etc... that flat-out rejects the Forgotten Realms "deities"... How? It's easy! Just keep reading page #56 of the 5e PHB, since it goes on to state: "Once you've chosen a deity, consider your cleric's relationship to that god. Did you enter this service willingly? Or did the god choose you, impelling you into service with no regard for your wishes?"
There you go... the Forgotten Realms "deities" can grant you spells, thereby enabling you to be a Cleric, but they can't require you to worship them!
Sounds like a great character idea to me!
...I'll circle back to the MTOF Elves in a subsequent post. (Spoiler Alert: It's all good.)