Im Christian, but I see a relationship here. All religeons that are based on one god worship the same divine being (likely excluding pure Bhudists (unless what I know is mistaken), and BTW the Budha was only a great philosopher who may have received God's enlightenment, not a god himself) that created this and all other universes, just in different contexts or names (it's more political than faith based to me). Polytheists may have simply mis-identified arch-angels, or other higher beings, as gods themselves (this theory may vary depending on if there are ET's).
And for those who worship nature, by praising and honoring God's creation, we praise and honor God, as nature itself is an extension of God.
In conclusion, oaths, pledges, etc. using the word God can apply to all religions.