as a previous poster pointed out in Ireland at the same time as Catholics were having huge families, Protestants were limiting their families.
If you're talking about post-independence Ireland, contraception was illegal from the early 1930s till 1980, when the situation was relaxed gradually. So anyone living in Ireland at that time, whatever their religious beliefs, was bound by the same law, and the same lack of availability of condoms, pill etc.
en.wikipedia.org/wiki/Contraception_in_the_Republic_of_Ireland
The Catholic position on 'artificial' contraception by which is meant anything other than the rhythm method (which is essentially abstaining from sex when you're fertile) because all sex acts have to be open to the possibility of contraception is laid out in a papal encyclical called Casti conubii in 1930, and the more famous one Humanae Vitae (1968). The date of the latter is no coincidence -- it was after the pill was being marketed internationally, and many Catholics (and priests) believed the encyclical would allow the use of the pill, and were horrified when the position stayed the same.
I don't think it's any particular mystery why Catholicism enforces a celibate clergy though in fact it did so quite late, 12th century. As well as setting its priesthood apart, making them more special, and requiring total dedication to God in the way favoured by Saint Misogynist-- Paul who thought marriage was only for those without the strength to be celibate, it also meant that the considerable wealth of the church remained centralised and was not passed down via inheritance to children. Before it made clerical celibacy a rule, there were various canon laws about forbidding priests' children to inherit.
From almost the beginning of the post-Reformation church, Protestantism was anti-celibacy, partly to differentiate itself from Catholicism, partly because it saw clerical celibacy as promoting homosexuality and masturbation -- hence married Protestant clergy.
(Though there are now a minority of Catholic married priests -- when women priests were allowed by various Protestant denominations, some married priests who weren't happy with this converted to Catholicism, and obviously remained married.)