How does the Commune spell work when cast by someone with the Ritual Caster feat or a warlock with the Book of Ancient Secrets invocation?

Question

The D&D 5e spell Commune is a Cleric spell that contacts the Cleric's chosen divine proxy and asks them three 'yes or no' questions. It is a ritual spell, so a Warlock with Book of Shadows or anyone with the Ritual Caster feat really can learn and cast the spell.

Let's say an atheist wizard uses the Ritual Caster feat to learn Commune (gaining Ritual Caster does not require belief in any pantheon) and then casts it (which can be done through an arcane focus). Who would she encounter? (If it helps, the Wizard belongs to the School of Divination.)

Answer 1

Let the GM decide exactly how the message manifests

The commune spell simply states:

You contact your deity or a divine proxy and ask up to three questions that can be answered with a yes or no...

There isn't any further description, so the GM could decide any sort of divine proxy they wanted.
Personally, I would say that whenever the text refers to "your god" or similar, it can simply mean "the thing that gives you magic" for a Warlock this would be their patron, for a Wizard it would be their studies (specifically their school of study).

As user @guildsbounty points out, you could have the spell contact Mystra, the goddess of magic and the Weave (if you're in a Forgotten Realms campaign setting).
Or as user @ZwiQ points out, you could have the spell contact Savras, the deity of divination.
As user @Ryan Thompson points out, you could also have the spell contact whatever deity was worshipped by the person who wrote the scroll originally.

There is also support for "your god" not needing to be an actual god; the section on "Serving a Pantheon, Philosophy, or Force" from Xanathar's Guide to Everything states:

In certain campaigns, a cleric might instead serve a cosmic force, such as life or death, or a philosophy or concept, such as love, peace, or one of the nine alignments...

The cleric's class features often refer to your deity. If you are devoted to a pantheon, cosmic force, or philosophy, your cleric features still work for you as written. Think of the references to a god as references to the divine thing you serve that gives you your magic.

Technically this quote only applies to Clerics, but as far as I can find, it's all we have from the rules for even a similar scenario. Overall, the GM could say the Wizard "worships" knowledge, or magic, or Divination specifically, and could have a god of one of those things contact the Wizard. I would say that since Love and similar things can be contacted through commune, Divination can be contacted as well; how this actually happens is up to the GM.

Answer 2

Given your comments on what atheism means in this context...

The wizard chooses a deity or proxy when casting the spell, or else it fails.

The entire effect of the spell is to communicate with a deity, and that's what it does. The wizard would either have to decide which deity he hates least at the moment, or is welcome to choose "none," in which case that's who answers, no one.