LOL What happens when 2 theme teams play each other, one plays Ordinary Day, 1 plays Damage Control and 1 team ignores DC, while the other ignores OD?

The way ignoring OD works is that it creates a situation where it is like the other guy ignores the other BFC.

In this case, me ignoring OD would be the same as you ignoring DC. The result is that you would be ignoring DC twice.

so would there be no objects?

From the FAQ:
So no objects at the beginning of the game.

Even If I OD it?

In the situation you gave, yes, because the opponent ignored your OD, meaning Damage Control is still in play for your opponent.

wow that feels a little lopsided...