"Draft beer, not people/soldiers/students/men/boys” is a saying that has been printed on many gift items, such as T-shirts and buttons. “Draft beer, not students” has been cited in print since at least January 1966. “Draft beer, not people” ("people" is perhaps the most popular phrase ending) has been cited in print since at least May 1966.
Wikipedia: Conscription in the United States
Conscription in the United States has been employed several times, usually during war but also during the nominal peace of the Cold War. The United States discontinued the draft in 1973, moving to an all-volunteer military force, thus there is no mandatory conscription.
However, the Selective Service System remains in place as a contingency plan; men between the ages of 18 and 25 are required to register so that a draft can be readily resumed if needed. In current conditions conscription is considered unlikely by most political and military experts.
9 January 1966, Springfield (MA) Sunday Republican, “It’s News to Me” by Herb Caen, pg. 15A, col. 1:
Those “Make Love, Not War” stickers have sprouted an offshoot visible in the windows of the men’s dorm at San Jose State: “Draft Beer, Not Students.”
20 January 1966, Austin (MN) Daily Herald, “Pot Pourri,” pg. 4, col. 4:
NEWEST COLLEGE sticker seen around campuses: “Draft Beer, Not Students!”
9 February 1966, San Diego (CA) Union, “Johnson Aloof: 200 Chant In Airport War Protest” by S. A. Desick,
Of course, there were the placards:
“Make Love, Not War.”
“Draft Beer, Not Men.”
4 April 1966, The Oregonian (Portland, OR), “Teen-Age Look In School Clothes Mildyl Different” by Joan Cook (N. Y. Times News Service), sec. 2, pg. 7, col. 6:
Here and there an independent soul asserts himself with a barrage of buttons. “Draft beer, not students,” “Make love, not war,” “U.S. drinking team,” “End the war in Viet Nam” and similar sentiments bedeck parka and sweatshirt.
Google News Archive
11 May 1966, The Blade (Toledo, OH), “Power Use Not Arrogance For U.S., Johnson Claims” (AP), pg. 1, col. 6:
The pickets carried such signs as “Viet Nam for the Vietnamese,” “Draft beer, not people,” and “Peace, not platitudes.”
27 July 1967, Chicago (IL) Tribune, “A Line o’ Type or Two” by John T. McCutcheon, Jr., pg. 14:
And above all, he did enough thoughtful writing to fill more than a dozen volumes, or the equivalent of about 100,000 placards reading “Make love, not war” or “Draft beer, not soldiers.”
On the Wisdom of Words
By Geoffrey Atheling Wagner
Princeton, NJ: Van Nostrand
DRAFT BEER NOT STUDENTS is a zeugma.