Of American-English origin, the phrase zero tolerance designates a stated policy of non-acceptance with regard to a specified situation, activity, result, substance, etc.

These are the earliest occurrences of the phrase zero tolerance that I have found, in chronological order:

1-: From the Lawrence Daily Journal-World (Lawrence, Kansas) of Wednesday 14^th February 1940:

Better Quality Is Sought in Potato
Spud Special Which Stopped Here Illustrates Modern Demands
[…]

The search for higher quality and more complete satisfaction of consumer demands were the keynotes of the program on the Union Pacific potato train which spent the afternoon here today.
Seed selection, disease control, handling and marketing were phases of the exhibits on the spud special. […]
Considerable attention was given to exhibits and discussion of bacterial wilt ring rot, most recent and said to be the most damaging disease ever to hit the Irish potato industry.
[…]
Northern states have set “zero tolerance” as the goal for certified seed potatoes which are as free of the disease as is humanly possible. Oklahoma and Arkansas have a strict quarantine ruling on the malady. Potatoes which have as much as one per cent infection of the disease cannot be sold for seed in those states.

2-: From an article by Stephen J. McDonough, of Wide World News, published in several U.S. newspapers on Sunday 5^th April 1942—for example in The Cincinnati Enquirer (Cincinnati, Ohio):

An Eastern Seaboard Arsenal, April 5—(Wide World)—Several thousand nimble-fingered girls are helping win the war by turning out the fine parts of antiaircraft shells, cartridges, and machine gun bullets for the ordnance department of the army.
[…]
The General who commands this ordnance arsenal is obviously proud that in his group of women technicians he has 70 girls with Bachelor of Science degrees and two Doctors of Philosophy. These experts work in the gauge-testing laboratories and in the optical shops. Their standards are so high that for the prisms and lenses of fire-control instruments, telescopes, and gun sights they cut and polish glass precisely to “zero tolerance,” which means that light rays passing through a 90 degree angle do not vary by more than one billionth of an inch.

3-: From a story published in several U.S. newspapers in September, October and November 1943—for example in the Tampa Morning Tribune (Tampa, Florida) of Sunday 26^th September:

Portland, Ore., Sept. 24.—(U.P)—A multiple tool holding device which decreases setup time in war plants 50 percent and makes it possible for inexperienced men and women machinists to do accurate work on fine tolerances is being produced in Portland. It is called “Zero-Tol”.
The device makes it possible to set four tools at once. After the tools are set up, they return to their exact positions without special attention from the operator. “Zero-Tol,” (a contraction of the words zero tolerance), makes a common engine lathe into a semi-turret lather.

The phrase zero tolerance has come to specifically denote a stated policy of non-acceptance with regard to abusive, anti-social or criminal behaviour, especially the use of illegal drugs—policy typically enforced by strict and uncompromising application of the law, and designed to eliminate such behaviour.

The earliest occurrence that I have found of zero tolerance used in that specific sense is from Admiral Says Goals Change in 30 Years, an interview by Herbert Cook of Vice Admiral James Francis Calvert (1920-2009), published in the Columbus Evening Dispatch (Columbus, Ohio) of Friday 11^th June 1971—the following extract is about “recent well-publicized problems with narcotics and unrest among midshipmen on the Annapolis, Md. campus”:

He says most of the nine midshipmen expelled from the academy last spring for smoking marijuana were not able to adjust to strict discipline.
“We’re running a tightly disciplined organization,” Calvert acknowledges, “and this is not a tightly disciplined society today. Many of our students come from a very permissive environment, and all of a sudden they’re brought somewhere where they’re accountable all the time. A lot of them say it’s just not worth the price.”
Will the Naval Academy or the Navy as a whole relax the current rigid prohibitions on drug use? Not likely.
“We have zero tolerance on it,” Calvert says. “We don’t want people out in the fleet who are going to use nerve-altering drugs and endanger whole ships and hundreds of men. We just can’t afford the risk.”