Ala. Code § 31-2-36

Any citizen of this state may accept and hold a commission or warrant or enlisted membership in the armed forces of the state and reserve components of the United States without vacating any civil office, position, or commission held by him. The acceptance or holding of any such military or naval commission or membership and the receipt of pay therefrom shall not constitute such holding of an office of privilege and trust under the government of this state and of the United States as shall be incompatible with holding of any civil office, executive, legislative, or judicial, or position or commission under the government of this state.