As far as I can figure, these groups still prohibit birth control within marriage: Old order Mennonites, the Amish, some independent Christian types, and Catholics. Not sure if the ‘quiver full’ thing is a group or philosophy. I don’t know of any nonChristian groups, at least to my understanding, but heck I’m no expert. It seems like a pretty uniquely Christian thing at this point, unless some of the other faiths also changed on the issue.
Freegards
Great and pro-birth control Christians find themselves in great company: including Planned Parenthood, the LGBTQ community, should we keep naming more?
Quiverfull is a subculture as well as a philosophy, and it includes a lot more elements than simply natural reproduction.
The United States birth rate is rising and Evangelical families in the Quiverfull movement (named after a verse of Psalm 127) are playing their part in the trend -- to the alarm of the greens, no doubt. A few weeks after the New York Times looked at the subject of large families, National Public Radio has run a feature on the movement, which comprises about 10,000 families, mainly in the Midwest and South of the United States.
NPR interviewed some families in Michigan. Kelly Swanson and husband Jeff say they didn't want any children when they first married, but then began to notice that the Bible gave special value to big families. Now they have seven children and would like more. They are leaving it up to God to decide how many they can handle. The average family at their church has 8.5 kids, which compares with a national total fertility rate of 2.2 children per woman. (In 1976, 20 per cent of American women had five or more children, but by 2006 that figure had fallen to 4 per cent.) - https://www.mercatornet.com/demography/view/4846