No. This is a common question with a simple answer. Simply ask the officer administering the oath to say “affirm” rather than “swear” and to omit the “So Help Me God” at the end. Note that this is your right and asking (rather than demanding) in advance (or in the middle of the oath) does nothing to limit your rights. This secular option applies equally to all government oaths, including the oath of office for military officers and ROTC/Academy cadets and even the oath for jury duty. Anyone denied this right should contact MAAF for assistance. If the officer says the “so help me god” portion, simply do not repeat that portion. Drop your hand because the oath is over. You may also choose to set up a new ceremony, initiate an Equal Opportunity complaint against the officer for such discrimination, and/or contact MAAF for assistance.
It is illegal and unethical to force someone to swear to god if they do not want to. The governing regulation here is the Constitution Article VI Paragraph 3 “no religious test shall ever be required as a qualification to any office”. Also, US Code Title 1 Section 1, right up front says “oath” and “swear” always include the option to affirm. Given this freedom, do the following two things:
If applicable, point them at AR 601-280 “The Army Retention Program,” Appendix D Paragraph 2k, which states specifically that the reenlisting soldier need not swear to god. Or to USC 512 Title 28 (Revision June 25, 1948 ch. 646, 62 Stat. 925) which clarifies that an oath of affirmation excludes the “so help me god” portion. Air Force should refer to AFI 36-2606 (Ch.3, 2. “Detailed Instructions for Completing the DD Forms 4/1 and 4/2”, Table 3.9, Item Number 15 – Confirmation of (Re)enlistment Oath). Each service has similar alternatives which may be unclear in written policy but should be made clear by any legal advisor.