Some of this information comes from Spike Tyson, Commander of the American Atheists Veterans. The Veterans of Foreign Wars of the United States Membership Application form has the following statement immediately above the signature of applicant field:
"I certify that I am a citizen of the United States, that my Campaign Service was honorable, that I have never subsequently been discharged from the Military or Naval service under dishonorable conditions. I further state that I believe in God ."The American Legion no longer has a statement on their membership form, which you must sign, stating that you believe in god, as they once and always did have. However, in order to be a voting member and, thus, to be an officer, you must believe in god.
It has been determined by the courts that the VFW and American Legion are "religious organizations" (incorporated by the federal government and for all veterans, no less) that have the right to discriminate against non-believers.
Another organization of this type which requires a belief in god to be a member is the Daughters of the American Revolution (DAR).
At a recent reunion of an Army division, Spike Tyson said that a person approached the podium and said "Of course, we know there are no Atheists in foxholes." At which time, Spike got up and protested rather loudly that there are, indeed, "Atheists in foxholes" (He also has several Purple Hearts from his duty in Vietnam and is a member of the Order of Purple Hearts).