Ancient scepticism was frankly opposed to religious belief.
But more important was the influence of philosophy, which led soon enough to a general scepticism among the upper classes.
But scepticism of this kind was not universal.
Like Socrates, he was not a philosopher, and did not pretend to be one; but, as the reasoned scepticism of Socrates cleared the way for the philosophy of Plato, so did Xenophanes's "abnormis sapientia" for the philosophy of Parmenides.
It remained for the more robust faith of a Schliemann to show that such scepticism was all too faint-hearted, by proving that at such sites as Tiryns, Mycenae and Hissarlik evidences of a very early period of Greek civilization awaited the spade of the excavator.