Non-biological entities do not necessarily have to be robotic creations of biological ET's, nor do they have to be "alien", as in extraterrestrial.
I believe the Catholic Church have already announced, on the record, they are comfortable with the idea of extraterrestrial life. In Islam there is the tradition of the Djinn, which is a being of fire or smoke (dusty plasma?).
So, depending on the nature of the contact, it is not foreordained that these organized religions would evince any immediate, strong overt negative reactions.
But, as Ivan noted above, the ET belief has the capacity to threaten conventional organized religion. The Brookings Institution once reported out that contact within our solar system could threaten our currently established civilization, and it may well be true that the CIA and other government agencies monitor UFO/cult activities for signs of social unrest. At one time, I think >50% of "ufologists" were retired from the CIA or other military intelligence agencies.