While it is never really conclusively said in the media, I think there are enough examples to say that the ties of FF to Catholicism, are argubaly stronger than that of the other parties:
1. The general crossover of modern republicanism with catholicism, and FF being the branded 'republican' party
2. The 'advice' given by JC Mcquaid to De Valera on the drafting of the 1937 Constitution, along with a very close working relationship between the two men
3. On this site, the majority of staunch 'pro-life' people who like to use terminology like 'baby killers' for those with a different view, have either FF avatars, or are 'closet' supporters.
4. Michael Woods - rumoured to be a member of Opus Dei - controversial compensation deal with the Cathoic Church on institutional abuse, while a Minister.
5. Dermot Ahern introducing a 'blasphemy law', while Minister for Justice
Are the others steeped to the same degree in conservative catholicism?
FG A mainly conservative party, but also one with a noticeable social democrat wing, over the years. Won the 'protestant' vote, over the years.
Labour Pro Abortion, pro gay rights, among other things.
SF Younger members tend to be left of centre.
Micheal Martin is obviously trying his best to market his party, as one for modern 21st c Ireland. But, some of the examples I have used are way too recent, to be able to get the feeling that FF has completely cut itself off from this thinking.