In my 20+ years in the Evangelical world, I have found that the percentage of ex-Catholics who went Protestant for the above reasons, is exceedingly small.
If anything it's the opposite: they're attracted to Evangelical Protestantism because that's whose actually teaching the Bible and biblical living. The Catholic church, by contrast, has really dropped the ball on Scripture teaching, despite St. Jerome's admonition ("Ignorance of scripture is ignorance of Christ").
As for contraception, (a) it isn't clear from the scriptures alone, but nevertheless (b) I do seem to encounter more non-contracepting, large, natural families in the Evangelical world than I do among Catholics... why is that?
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."
I have been a Catholic for 75 years and prior to Vatican 2 one never heard of Catholics leaving the Church to enter an Evangelical Church or the Evangelical World. I am sure you will find those who left the Church are/were all post Vatican 2. Why, because that era until the last 10 years lacked any catechetics. The Church failed on teaching its ways and certain religious started the Church in the wrong direction.
Every person, in most part, I knew in those years who “fell” away from the Church were caught up in poor marriage situations. They were not strong in catechetics nor in beliefs of the Church. They therefore felt no qualms about leaving. These and other people, if they practised their faith, also got tired of confessing about their contraception so they also left.
These people still wanted a Church affiliation so they looked for a church that condoned divorce and remarriage and contraception. So they found another Church that overlooked remarriage. I don’t think these people are born again if they have committed unrepented adultery.
<<<”I do seem to encounter more non-contracepting, large, natural families in the Evangelical world than I do among Catholics... why is that?”>>>
That is a perception that no one can answer. I was born before the great contraception age as was my cousins. I was an only child, my aunt had 2 boys and my other aunt had 1. It was also before any form of natural planning was instituted. Having 1, 2 or 10 children does not mean much. My mother and aunts and the whole family were staunch Catholics. We also lived among Hasidic Jews who had 10 plus children. Even today, one can live among Muslims and only have 1 or 2 children where the Muslims have 7 or 9
Whether one group has more children than the other does not affect the cause for leaving the church.
I wonder if you have been to a Catholic Mass? A Catholic Mass is served every day of the year. There are two scripture readings and teaching per weekday and 3 readings
and teaching on Sunday. That is 15 scripture teachings per week. I believe other denominations might have as many as 3 to 6 per week.