I think there would be an increase in religious militancy from several creeds; the confirmed arrival of some alien civilisation would likely threaten their construct of our world, it's past, and the universe, as well as the nature/identity of God.
Also, being a lifelong student of history, I fear a 'Saxon Effect'. When Rome evacuated Britain, to become buried in it's civil wars, the romanised celts (Britons) needed help fighting off raids from the 'wild' Celts of the north and west; they turned to two (Saxon, I believe) chieftains from outside for help. They got it, but then the 'helpers' decided they didn't want to leave, and stayed...thus began the destruction of romanised celts of Britain.
Our history is full of similar examples; several native Amerind tribes sided with the european colonial invaders against their native neighbors..tribes 'used' the colonial power against their old enemies, and were then swallowed up/beaten down by their new 'friends'. Same thing in Africa...europeans usually found help from local tribes in attacking those tribes' old enemies, only to discover their 'friends' had become overlords.
An alien civ would not have to be looking for colonising/empire building here, but could be 'used' by one Earth faction against others, and then find they had made enemies that had to be 'dealt with'.
Whether the ultimater outcome turned out good or bad, it would be a very dangerous time.