To my understanding the only religious groups that currently oppose contraception within marriage are Christian. The only Christian groups that still officially ban it within marriage that I have found: Old order Mennonites, Amish and Catholics. I think the ‘quiver full’ movement might encompass individuals from many different groups. And of course there are many individuals who don’t accept it for their personal religious beliefs.
Freegards
It is neither weird nor offbeat to hold to what has been the mainstream Christian stance until the mid 20th century. Not holding to it at large has caused tremendous damage to the ‘basic’ Christian witness for the last half century plus and now it is time to stop the damage birth control has wreaked on almost every facet of society in its tracks. And take responsibility.
It does not mean everyone is supposed to have massive families.
You are correct. Quiverfull is trans-denominational.