The largest families I know are Catholic... and I'm talking they don't stop at 2 or three.. but rather popping out another and other every couple years (or less) until menopause... I missed his recent guidance on reducing the population in support of climate change...
*shrug* - Personal experience I guess. Largest ones I know are Mormon - or rural. As in Iowa farm boy with 20 siblings.
I don't think "The Waltons" were Catholic, but I knew rural families like that.
I think there's more culture associated with Catholic and family size, because France is largely Catholic but I don't know of large French families, but I do know of Italian families being large - BUT - my Roman history I took in college is that THAT has been that way for thousands of years.
I know people want to believe it's because of Catholicism and birth control, but honestly modern birth control is a recent thing historically, and large families go back centuries.
Prior to modern times, Asian and Indian families were large, and they're not known for being Catholic.