But reading your OP you seem as incensed by a catholic ethos being promulgated in church run schools as you are with discriminatory access. IMHO the (vast) majority of Irish people do not agree with you on this point and the state has no role in subverting that poular wish.
Religious belief being based on faith is inherently irrational.
How far should a republic based on the ideas of the enlightenment go in supporting religious education.
In Britain, there is at least one Jewish school who suggested recently that mothers should not drive their children to school as women shouldn't appear in public. http://www.theguardian.com/uk-news/2015/may/28/hasidic-sect-london-mothers-stop-driving.
Do you think that the state should have no role in subverting that wish.