The American-English expression birth-control glasses and variants (also BCGs and variants) denote ugly spectacles, in particular army-issue spectacles.
The image is that those spectacles are so ugly that nobody would want to make a baby with somebody wearing a pair.
—Cf. also men seldom make passes at girls who wear glasses, John Lennon spectacles and to go to Specsavers.
The earliest occurrences of the expression birth-control glasses and variants, and BCGs and variants, that I have found are as follows, in chronological order:
1-: From Just wait until Brigid comes marching home again, by Lynn Bartels, published in The Albuquerque Tribune (Albuquerque, New Mexico) of Monday 15th December 1986—the following is an excerpt from a letter that Lynn Bartels’s sister, Brigid, wrote about life in a military training camp:
Feb. 18—Tomorrow I pick up my BCGs. BCGs are our eyeglasses. BCG stands for birth control glasses, because no guy would look at you in these things. They are black horn rims.
2-: From Getting that geeky look: Nerd glasses may be an eyesore but many think they’re out of sight, by Holly Mullen, published in the Spokane Chronicle (Spokane, Washington) of Thursday 27th August 1987—Diane Newell is an apprentice optician; she may have independently coined the expression birth-control glasses:
The comfort factor sold Newell on nerd glasses eight years ago. “They’re small and lightweight. I wore them all through school and I still wear them in the shop.”
For Newell, the trendiness of the glasses is just icing on the cake. Now that they’re hot, she no longer feels a need to defend them.
“It’s making it a lot easier to wear them. I used to call them my birth control glasses. They’re so ugly that when I wore them I never had any trouble keeping strange men away.”
3-: From the column Around Town, published in The North County Blade-Citizen (Oceanside, California) of Sunday 13th January 1991:
Passes with glasses…
Troops in Saudi Arabia, or anywhere else for that matter, have a special name for the plain, brown, horned-rimmed prescription glasses issued by Uncle Sam.
The specs are called B.C. glasses, or birth-control glasses, because it’s unlikely anyone of either sex will get a date while wearing a pair.
4-: From a glossary published in several newspapers on Saturday 9th February 1991—for example in The Times-News (Twin Falls, Idaho):
IN NORTHERN SAUDI ARABIA (AP)—Wars tend to create new words, phrases and acronyms, and the Gulf War is no exception.
Here is a random sampling of some of the war words exchanged among troops in Saudi Arabia:
BCD’s (for birth control devices): Glasses, used to describe ugly military-issue spectacles.
Bob badge: A Purple Heart, the medal awarded to U.S. soldiers wounded in action.
Bullet-stoppers: The U.S. Navy’s term for the Marines.
[&c.]
5-: From Reserves: Desert Storm here we come, about the departure for Saudi Arabia of the 685th Terminal Transportation Army Reserve unit, by Toni Griffith-Byers, published in The Vidette-Messenger of Porter County (Valparaiso, Indiana) of Sunday 10th February 1991:
Sgt. Daniel “Shredder” Roe, 29, from Lakes of the Four Seasons, hugs his wife, Lynn. […]
[…]
Shredder, wife in arm, is in an ebullient mood. It’s a good thing he’s already married, he teases, taking off his own glasses and donning thick, horn-rimmed Army issue spectacles.
“We call them B.C. glasses—birth control glasses. There’s no way you can get a date wearing glasses like that.”
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