Yes, I kind of got that the pronunciation mattered.
Sorry, I forgot the R. There are two Rs in my name and French people struggle to say it at all, with their beautiful rolled Rs.
Liadan? I struggle with that one because of the broad D. English people won't say it right, but French people might.
"It's just that I have been told that Caitlin can be pronounced Catlin by Irish speakers in some parts of Ireland."
In terms of vowel sounds, yes. But the problem with the pronunciation of the narrow T sound remains in all dialects (unless you are prepared to accept the Irish pronunciation of people who don't speak Irish very well and commonly mispronounce words).
This would be a problem in Ireland nearly as much as in France.
It's just not a sound that exists in English and most Irish people won't say it properly when speaking English, and many of them don't even know how it should be pronounced. The whole beauty of the name comes from the sound of that narrow T IMO.
Personally I would say that if you're not an Irish-speaking family, steer clear, and if you are and it will bother you that the vast majority of people with butcher the name, still steer clear.
Or if you don't care that Catlin is only a vague approximation of an Irish name, then use that.