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In a way the movie seems a bit of a mea culpa for mainstream Protestantism missing the boat. “Opposition to birth control was seen as a Catholic thing,” one commentator says. “Protestants were for liberty.”
Having worshiped in conservative Reformed churches for the last 20 or so years I will say that each of them puts great value on large families and are against oral contraception. So my data point is 3 PCA churches, a United Reformed Church of North America congregation and an ARP church.