Given that one of the charges against Socrates was atheism, one suspects that belief or faith along with following the forms was important to at least some of the Greeks. My brief internet search indicates that this seems to be largely true of most of the polytheistic religions.
It seems more like the ancients typically didn't make much of a distinction between faith and ritual. Why wouldn't you do the rituals if you believed?
And of course within Christianity, there has long been a debate as to which was more important, faith or works and whether works alone can get you into heaven. Catholics being somewhat in the middle on the matter while protestants seem to go hard one way or they other depending on denomination.