Recently, our daughter (17 in June) told my wife and me that she has started dating not 1, but 2 guys. No introductions needed since we already know them; they’ve been close friends of hers for quite some time now. Daughter put it as: why do I have to choose if I like them both and they don’t mind sharing?
I just don’t like it.
Being worried about such a set up, especially with teenagers, who are emotionally and physically underdeveloped, where things going wrong can have life long consequences (STDs, unwanted pregnancy, trauma from emotional/physical/sexual abuse), it is perfectly reasonable to be worried, without it having anything to do with puritanism or christian fascism. These consequences are already possible with a monogamous relationship and get more likely with poly relationships.
It should be the parental instinct to be worried about their teenagers getting romantically active and to watch out for their children, without directly preventing them from doing thing or forcing them into hiding. It is only logical that this instinct gets more worried if not one but two, or even more people that could be a threat to their child are involved.