Of course this will likely vary by country/region. Was raised Catholic in the US, then distanced myself from religion on account of bigotry/abuse/hypocracy in the local church (and my agnosticism). Now, my path has led me to consider PhDs in Europe, and Catholic universities have come into question.
I avoided catholic universities when looking for my undergraduate school, as I knew a religious school would come with more socially conservative people and more rules/pressures to behave a certain way. I did look at a jesuit university, but some of these tend to me more open-value and less tailored to christianity.
My impression is that Catholics in Europe tend to be more morally aligned with Christian tradition in a cultural and sometimes intellectual sense. The church may be corrupt everywhere, but at least people personally are not completely hypocritical in their lifestyle. Whereas in the US, I see catholicism and its controversies aligning more with the alt-right/evangelical wave, or the "trad cath" trend. Of course, everywhere has a diversity of interpretations and people will always apply their beliefs and values in different ways.
All this is to ask: what is the reputation of Catholic universities in Europe? of course you don't have to be catholic to attend. But does seeing it on a CV raise any thoughts whatsoever? It seems to be more of an affiliation with no particular pressures, whereas in the US I might make judgements about a person (of course I shouldn't, but it's a defensive instinct)