Meaning, in the U.S. it's Jehovah, but in Saudi Arabia it's Allah?
Seems a bit vague to me. I got the impression lower case alluded to an unspecified deity even if a specific is presumed / implied. Upper case more of an endorsement of the supernatural, yet still short of a specific deity, unless otherwise indicated.
ref:
I pledge allegiance to the flag of the United States of America and to the republic for which it stands, one nation under God, indivisible, with liberty and justice for all.
This, the current official version of the Pledge of Allegiance, has developed from the original pledge, which was first published in the Sept. 8, 1892, issue of Youth's Companion, a weekly magazine then published in Boston. The original pledge contained the phrase "my flag," which was changed more than 30 years later to "flag of the United States of America." A 1954 act of Congress added the words "under God."
The authorship of the pledge had been in dispute for many years. The Youth's Companion stated in 1917 that the original draft was written by James B. Upham, an executive of the magazine who died in 1910. A leaflet circulated by the magazine later named Upham as the originator of the draft "afterwards condensed and perfected by him and his associates of the Companion force."
Francis Bellamy, a former member of Youth's Companion editorial staff, publicly claimed authorship of the pledge in 1923. The United States Flag Association, acting on the advice of a committee named to study the controversy, upheld in 1939 the claim of Bellamy, who had died 8 years earlier. The Library of Congress issued in 1957 a report attributing the authorship to Bellamy. / The World Almanac and Book of Facts 1997