There is a sizable group of Protestants who appear to me to be ahead of the curve on the fundamental issue of male/female roles, what is sometimes called "complementarianism." Understanding and then living this basic principle is a necessary precursor to having "large, natural families."
Unfortunately, this whole concept has been lost in the Catholic Church for the past 40 years. Catholics have been divided into 2 groups: the liberals who are busy contracepting, fornicating, etc, without qualms; and the "conservatives" who have followed JPII's lead into the quagmire of "mutual submission."
The only Catholics who follow the Biblical mandate for male/female roles are Traditional Catholics who have rejected the modernistic changes that have happened in the last 40 years since Vatican II.
Since Traditional Catholics are a small percentage of the overall Catholic population, what you've observed regarding evangelical Christians versus Catholics is not too surprising. If one attends Mass at a Catholic Church that uses the "New Mass," one is unlikely to see any "large, natural families." If one attends Mass at the traditional Latin rite, in contrast, virtually every family there will be a "large, natural family."
So much for true Christian witness.
Most other ex-Catholics I know are ex-Catholics because they cannot live with the Magisterium and got tired of being cafeteria Catholics.
I see far more ‘large natural families’ at every Catholic church I attend than I ever saw at the prot churches I used to frequent.