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.
Things feel weird, strange or unnatural because they go against instinctive feelings.
As for why they are more likely to go wrong it is quite simple. Two teenagers are more trouble than one teenager. Especially if they are in competition with each other. Jealousy is a key driver for violence and young men are the demographic generally most violent. These are things that you know subconsciously, as you have most likely experienced them yourself. As for negative experience with men and in particular men seeking sexual contact i think every women will be able to confirm danger and or having experienced abuse themselves. Now you have two rabbit-horny high on testosterone teenagers that have to “share” one teenage girl. This should cause an instinctive negative reaction by every parent.
As for studies which analyzed the situation where one men has multiple women concluded that these relationships negatively affect the women and their children psychologically.
https://pmc.ncbi.nlm.nih.gov/articles/PMC8667458/
Now this of course is different compared to a situation where one women has multiple men. A situation which seems to be much less prevalent and i couldnt find studies on quickly. As to why they are much less prevalent, this gives reason for even more worry. There is reason to believe them to be less stable and likely end up with violence, where women on average a physically much less stronger than men.