The idea seemed radical and intriguing to me when I first read it at HBDChick years ago, that the Catholic Church's sanctions against cousin marriage had created enormous downstream effects, which extend even to changes in the population genetics. The thought was that this weakened kinship power, which tends to keeping resources and power in the family. (She also identified feudalism as having a similar effect. One's loyalty is to the lord, the landowner, rather than the clan leader.)
I am now hearing reference to this theory in many places. It seems to have gained acceptance as one explanation for the WEIRD phenomenon, as in Harvard social scientist Joseph Henrich, and be treated as established by some modern geneticists (as interviewed on the genetics podcasts I hear and articles I read. They seem to be top guys and gals, not fringe) that this has increased gene frequencies for traits of cooperation, including those that have impact on welcoming strangers.
I don't know if this is a cause or a result, but the tradition recorded in Beowulf and records of similar age that thanes gave their support to the many minor rulers freely but conditionally is important in this context as well. If a warrior felt his lord was not living up to his obligations, he could choose a different lord. This does not happen easily in clan-based or family-based societies, even up to the present day, such as much of the Middle East. Beowulf may be imposing the ideas of the 10th C back onto the 8thC or 6thC in this, but that doesn't matter much for our current discussion. The entirely patriarchal authority of a clan leader trying to protect resources for his group gave way to what are called "third-party institutions," such as the church, guilds, market towns, and independent trading networks such as the Hanseatic League and its network of cities. Even banditry is an expression of independent organisation outside the previous structures. Whole tribes might ally themselves with the declining Western Roman Empire in the 5th C, but there were also many examples of individuals, especially from Germanic tribes, enlisting in the Roman forces. This independence increased steadily over the next 1000 years. Admittedly, this was intermittent, as crises of famine and plague would send individuals back to submission to group protection and rules. (Which is fine. Independence is great, but people gotta eat. Your sons can resume independence - because they survived.)
While family ties constantly reasserted themselves within those contexts - noble families giving sons to the church and receiving influence in return, up to the level of the papacy, or passing along guild membership to sons - but this was no longer as strong among Europeans.
So there was gradually less intracultural violence starting from at least 13th C and maybe even earlier. Women gradually enjoyed higher status and more rights, as they had more say over who they would marry, or weather they would marry at all. That was not likely intended, but you can see how it would happen. It's the Hajnal Line again, with both men and women marrying later, being closer in age, and women sometimes even not marrying, or not remarrying if widowed. These are the areas of decreasing cousin marriage and clan power and increased feudalism.
Just so you know that it has moved from fringe belief to minority opinion among traditionalists and majority opinion among newer and younger researchers.