Two clarifications:
The god part of the oath is optional – MAAF FAQ – Opting out requires a person to ‘out’ themselves to their superiors, which can be hazardous. If even the perception of discrimination is there, service members may be forced to adopt their leader’s religious oath. But it is technically optional.

“Atheist” whether you call it a religion or not, is included as a special ‘religious’ group that must be tracked and supported by the military chaplaincy for purposes of morale, welfare, and command climate. Failing to include atheists and other secular Americans is creates a rift in the military by excluding large swaths of the population. – MAAF Chaplain Outreach Program

All that having been said, please see below 2 organizations working to free the military from the clutches of Dominionist Evangelical Christians and Two organizations that show very clearly that these forces exist and are actively and very successfully co-opting our military as a venue for spreading their personal religious beliefs.
Military Religious Freedom Foundation
Military Association of Atheists & Freethinkers – (with a longer list of ongoing problems)
Campus Crusade Military Ministry
Officers’ Christian Fellowship

This is a huge issue and one that needs a lot of focus and support from the nontheist community, and from Americans who would rather their military supported America rather than Jesusland.

Jason
MAAF