I suppose the main thing is that the more Europeans began to learn about other societies, the more they realised the way they did things was not the only way.
Of course, Europeans had always been aware of the Islamic empires to the south and east and people knew of far off China and India but not much about them.
I don't know if knowing of other cultures ever made people feel more European, but perhaps it more sharply defined "Christendom" - the idea of the group of Christian nations ruled by the morals of the Bible, and people describing Christian government would usually contrast it with the despotic non-Christian empires of the East.
It wasn't until quite late, i.e. 18th century that the concept of people worshipping different gods in different places really served as an idea with which to undermine the dominance of Christianity,
Definitely by the 18th century people were using examples of other societies - savage societies - to make a critique of European decadence, immorality and bad government.
