I live in Ireland and think it's a fantastic place to be. My husband is a high earner though so that helps as our life is comfortable enough. So things like paying so much for the GP/prescriptions is annoying but not an issue. That said, i only go if I'm really sick and might save up a few ailments. If you earn below a certain amount you get free GP.
There are some nondenominational schools and multi-denominational schools. They can be very difficult to get into due to high demand and often work on a lottery system rather than catchment.
Catholic schools aren't like faith based schools in the UK. Yes there are school masses and the odd prayer here and there but in my 14 years of Catholic schooling here i don't think i ever saw a bible.
I think the "people are conservative" comment is out of date. I would consider Northern Ireland to be conservative but the Republic is much more modern.
University is not free anymore but it's not as costly as the UK. They call it registration fees and it can be a couple of grand a year.
Housing is where you'll hit a brick wall. It is nigh on impossible to find somewhere to rent and when you do you'll be paying €2k per month for a small 3 bed in a not great area. (Dublin. Not sure about the rest of the country). Buying is also difficult as there just isn't enough on the market to meet demand.
Groceries, eating out, clothes - all more expensive than the UK but wages here appear to be higher.
You will have no problem being an English person here if you're living in a city. In the countryside it could be noted that you're foreign and it may be harder to integrate.
Child benefit is a lovely bonus every month but i wouldn't factor it in because as pp's said - tax is higher and almost everything costs more.
Still, great place to live with great people and i think the education system is fantastic. You just need to be earning the (fairly) big bucks to have a fairly normal standard of living