I think you're right there - I think your average person, 'The Plain People of Ireland' as Myles na gCopaleen used to say, have never really bought into the whole TWAW-self-ID thing.
I don't think it's based on residual Catholicism - though it is worth noting that the Catholic church has never wavered from its opposition to transgenderism, on the basis that it denies the dignity of the human being as created by god [I'm just quoting, not agreeing!]
We have a small population, so if less than 0.5% are trans - 0.2% may be more realistic - that's a very small number of people, and the mathematical likelihood of a trans identifying male trying to get onto a local women's rugby is small.
But in any case, they wouldn't be allowed in as the IRFU policy is
contact rugby for players in the female category is limited to those whose sex was recorded as female at birth.
Other sporting bodies have 'trans inclusive' policies.
I think most people have been able to tootle along with gender ideology being in force at a high level in legislation etc, but not affecting them on an everyday level.
When it has done so, there has been pushback, e.g. opposition to unisex toilets in schools, Barbie Kardashian being in a woman's prison [he was later moved after public outcry]. A proposal to limit the specific references to women in the Constitution was heavily defeated last year.
And yet, and yet.... as I said upthread, it looks like an openly full-on TWAW candidate is going to win the presidential election.