Can you cast a commander from the command zone if it has been turned face down?

A commander in the command zone is always a face-up, fully visible card. The command zone is not a zone where cards exist face-down in any meaningful game sense — face-down status is a battlefield (or stack) concept tied to effects like Morph or Manifest (CR 707.2). A card sitting in the command zone simply cannot be in a face-down state that affects how it is cast.

When you cast a commander from the command zone, you are casting the card itself, with all its characteristics visible and applicable (CR 903.3, CR 601.2). There is no game mechanic that allows a card in the command zone to be turned face-down and then cast as a 2/2 vanilla creature the way Morph works on the battlefield.

If a commander has the Morph or Disguise keyword, you may cast it face-down from your hand (if it somehow ended up there), but casting it from the command zone always means casting it face-up as its true self. CR 707.4 specifies that you may cast a card with Morph face-down only when you could normally cast it — and the casting from the command zone does not grant any special face-down permission.

Concrete example: Your commander is Ixidor, Reality Sculptor, which has no Morph itself. Someone jokes you can 'flip it face-down in the command zone' to hide its identity. This is not a legal game action. When you pay the commander tax and cast Ixidor from the command zone, it enters the stack face-up with all its characteristics.

In short, face-down status does not apply to cards in the command zone, and casting a commander always produces a face-up spell on the stack (CR 707.2, CR 903.3).