I checked question 40, "which are the issues that most create a feeling of community among European Union citizens?", where religion was way back with 13% in the EU-27. Members and candidates with significantly higher figures:

Turkish Cprus: 49% (most frequent choice)
Turkey: 41% (most frequent choice)
Romania 28% (2nd most frequent choice)
Malta 26% (4th most frequent choice)
Cyprus 25% (3rd most frequent choice)
Slovakia 25% (3rd most frequent choice)
Croatia 21% (3rd most frequent choice)

So, interestingly, religion matters most just in the candidate country that might be resented for that, and is high in some new members least sceptical of Turkey's accession. (BTW the question is not nuanced enough to know whether Turkish citizens thinking so are Eurosceptics or those who would join and think religion is why they get rejection.)

_{*Lunatic*, n.
One whose delusions are out of fashion.}