As has been written in some earlier threads on this subreddit, Greek mythology might not have been very important but Greek religion definitely was. It is also difficult to know the average person's perspective since so much of our sources come from aristocrats.

In this answer u/UndercoverClassicist describes elite scepticism of Greek myths, but that the mythology was often presumed to be basically true. And here our u/Iphikrates writes about the ample evidence we have that the ancient Greeks considered their religion and gods important, and also that the myths were not the most central part of the religion. If you want to learn more about the difference between religion and mythology more generally you can read this answer by u/itsallfolklore. Further answers by our users are of course very appreciated, especially if they can give information on belief among the lower classes.