I've disliked Heinlein's version of poly (line marriages) for several reasons, mostly because I don't think it would work out as comfortably as he claims it would. However, various societies have had, or continue to have, several versions of group marriages/polygamy and I think we should look to those to see what possible problems arise.
As for the incest crowd, I have no idea what the hell is going on there. Unless it is the triumph of Slaanesh, where all loves must fall and be absorbed into the one ruling love that outweighs all, which is the Infernal Venus, and even parental/familial love has to be dissolved in those waters and be cast anew as sexual/romantic. We have crowned personal gratification as the highest value, discarded the very notion of taboos, and labelled any opposition as -phobes and -ists, the one remaining sin society is willing to classify as sin, to be a -phobe and/or an -ist.
As C.S. Lewis warned in "The Four Loves", any love when exalted out of its proper place turns on us:
We may give our human loves the unconditional allegiance which we owe only to God. Then they become gods: then they become demons. Then they will destroy us, and also destroy themselves. For natural loves that are allowed to become gods do not remain loves. They are still called so, but can become in fact complicated forms of hatred.
He sums it up elsewhere in the work as "When Love becomes a god, it becomes a demon". And now that we have elevated sexual love to the status of Supreme and Only God, it is showing its demonic nature in such groups and appeals and soft-soap sob-story articles about (Not Real Name) and (Not Real Name), siblings who never knew one another until they were adults, met, fell in love, and are now wrecking both their marriages and families because they can't resist the siren call of fucking one another - ah, but this is the fault of nature, of their genes! There's even a name for it and, God have pity and mercy on us all, an information leaflet by a British county council.
I think when we've come to the point of needing leaflets warning "Just a heads-up, but if you're facilitating a meeting between an adopted person and their birth family, be aware that some of them may decide to fuck each other", then something has come loose in the machinery of society. Also, all the jokes about rednecks in Southern US states being in-breds are losing their bite; it seems that soon, confining the blending of sexual and family bonds to your first cousins only and in no closer degree will be positively quaint.