During the Vietnam War, there was conscription in Australia. I'm just wondering, under that system of conscription, whether a politician, assuming they were otherwise eligible, could be conscripted if their birthday was chosen?
I can't answer for Australia, but I'll answer for the United States.
During World War II, a young (draft-aged) Congressman (and future President) named Lyndon Baines Johnson wanted to volunteer for the U.S. army. President Franklin Delano Roosevelt was horrified at the thought that an American Congressman could be killed, or worse, captured in battle. The President threatened to intervene with the Armed Forces to reject Congressman Johnson, who then withdrew his application.
Politicians at the level of "Congressmen" or higher would be considered too valuable to conscript. Maybe a very low level politician such as an assemblyman might be called.
From The national service scheme, 1964-72, it is implied that a politician cannot be a member of the military during the time they stand for election and for as long as they hold elective office. Neither the National Service Act 1951 nor its amendment, the National Service Act 1964, mention an exemption for officeholders.
Full-time Regular Army officers and men serving in the armed forces who wished to stand for election or to take a seat in the Commonwealth Parliament had to be discharged before standing for election. Initially, national servicemen could not be discharged for this reason. Before the 1966 election the legislation was altered so that national servicemen who were 'bona fide candidates' could be discharged to contest it at the discretion of the Military Board. Three stood for seats in the 1966 election. One was 21-year-old Brian King, who had made numerous unsuccessful attempts to be granted exemption from national service. With the support of Youth Campaign Against Conscription, King stood as an Independent against the Minister for Labour and National Service, Leslie Bury, for the Sydney seat of Wentworth. King was unsuccessful and performed the rest of his national service.