Polyamory is a concept fairly new to widespread social discourse and as one can imagine, divisive. Being no expert on the practice myself and leery of spreading misinformation, I entreat you to seek out the information yourself ( you are on the interwebz, after all). Do it. I won't spoon-feed you information.
Back from your research? Fantastic.
What I want to address is the representation or rather, what I perceive to be the misrepresentation of the practice in video games recently. Most notably, the incorrectly perceived depiction in Fallout 4 and why everyone's beef or applause is sorely misplaced.
Fallout 4 is the first Fallout title to allow for a sustained romance with a companion character, whereas the prior titles only approached intimacy as casual encounters or prostitution. Moreover, the game "allows" the player to sustain multiple romances with multiple companions provided that the player can get the companion in question's approval high enough and complete their personal quest.
I use the word "allow" with quotations because it is not so much a conscious choice on the part of the game but rather a technical failure which prevents the companions from registering the fact that the player is involved in other romances.
For instance, it is not that the game recognizes that you are in a romance with Cait AND Piper AND Hancock and is totally cool with it, but rather that the companions themselves are not privy to it.
A telling feature being that should the player, for instance, flirt with Romance B while Romance A is in the party, Romance A will disapprove of the action but never register Romance B as an actual romance.
The issue began with certain people taking this misrepresentation of polyamory due to a design flaw as a representation of the practice and spread the word. Conversely, others who disagree with the practice lashed out in response, both sides unaware that this was not an actual representation of polyamory at all.
Polyamory requires candid communication between partners regarding the existence of the other partners - Fallout 4 does not have this. You can technically romance all companions at once (Save for Codsworth, who cannot be romanced) but they will never acknowledge or register the other romances. Thus, it is is not a matter of genuine polyamory but each romance existing as it's own isolated experience.
Now, my acknowledgment of the design flaw that facilitated this interweb beef is not a harsh criticism. I'm actually very glad to see that Bethesda is branching into legitimate romances for the first time in the Fallout titles and that may indeed be why it was not implemented as well as it could.