While there were penal acts against Roman Catholics in Ireland, they were less severe than in England, and aimed at excluding them from official posts and owning land. Unlike England, the religion itself was not criminalised, and its marriages were (always, I think) recognised as valid.
Mixed Protestant/Catholic marriages, however, were explicitly invalid from 1746 to 1870 unless carried out by an Anglican priest. The act that disestablished the (Anglican) Church of Ireland was passed in 1869, so from 1871 its legal status was the same as any other church - thus the marriage law had to be changed. Civil registration of marriages had been extended to RC ceremonies (and all others) in 1864.
As Peter says, having two marriage ceremonies was common is such cases. Since the RC one was not legally recognised, it does not really matter whether it was called a religious marriage or something else (e.g. a blessing).