Small children can figure out whether the teenagers and adults around them are sexually more out-of-control or more restrained. They probably put out different levels of pheromones, and their voices, facial expressions, mannerisms, and other body language are all in a different direction too. Do the older people seem awkward or hesitant to touch each other (like hover-handing), or is it more like they can't keep their hands off each other (like when every dude used to walk around in public with his hand on his girlfriend's ass)?
More indirectly, when little kids are exposed to popular culture, they can tell what resonates with the majority -- songs that are emotionally hotter or colder, movies that have more or less T&A, and so on.
Although these things, just to name a few, do not make the kid entirely certain that the grown-ups are promiscuous, it does incline their beliefs more in that direction. On that basis, one of the first things they'll do -- or not do -- is start getting practice with courting the other sex (flirting), as well as advancing in what they do physically (kissing, playing "I'll show you mine if you show me yours"). It's like speaking a language: if the community speaks English, then English it is, and if the community is promiscuous, then prepare to enter that way of life too.
One major consequence of living in a more promiscuous group is that there's a higher probability that your siblings are actually half-siblings because your mother had you all by more than one father. Therefore, in time periods when promiscuity is rising, so should sibling rivalry, and both should fall together too.
By the time I was a child in the early-mid 1980s, the tiny spark of promiscuity that started circa 1960 had spread farther and reached a hotter intensity, to the point where it wasn't just marginal sub-cultures behaving more liberally. My memories of sibling rivalry are also that it was very strong back then.
We have a home video of me, around 4 years old, running around the back yard and clothes-lining my little brothers (who were around 2). It was routine enough that my dad, who was filming it, didn't try to stop me or punish me after the fact, but just made me go over and hug my brothers, say I was sorry, bla bla bla, that was totally insincere. My mother tells stories about how I used to reach into their cradles and pull on the blankets they were wrapped in like a rip-cord and send them spinning and spinning. Then there was something else that I can't recall off the top of my head, something about putting things in there or messing with the cradle or stroller so that they'd have trouble breathing. She says she was truly worried that my little brothers might not make it to 4 years old.
But it wasn't just me -- they started all kinds of shit too when they were old enough. I remember being chased around the house with Cutco knives, for one thing. Their harm didn't even have to come from their own hands: once my brother lied to my mother that I'd done something wrong to him and started crying, so she slapped me right across the face. He started laughing right there, which is a rookie mistake because then my mother knew he'd made it up, and slapped him too, after apologizing to me.
You get the idea. I don't see any of that stuff going on anymore, at least among children in public. When I visited my 4 year-old nephew a few weeks ago, I didn't see him do anything to his little brother that was as brutal as what we used to do. And his little brother is actually a half-brother, so that's an even more striking sign of how little sibling rivalry there is these days. Sure, he calls him a stinky baby whenever he starts crying, but nothing close to what I did to mine nearly 30 years ago. Certainly nothing violent or physical.
There are no surveys of how intense sibling rivalry is in each year, but my impression is that it had already begun to subside during the '90s, which would fit with the larger drop in violent crime and promiscuity. I just didn't see the little kids around the neighborhood clothes-lining each other when I was in high school during the second half of the '90s.
In popular culture, the little hell-raiser character disappeared as well. There was a Dennis the Menace cartoon show in the late '80s. Even the original was from the first year of rising-crime times, 1959, although Jay North was relatively tame compared to the kids in the '80s cartoon. (I saw the original series in syndication on Nickelodeon in the late '80s.) Then there were those Problem Child movies from the early '90s before the crime rate began falling. And of course Bart Simpson's early incarnation as the little hell-raiser during that period, before he became just another dorky smart-mouthed kid. This stock character didn't exclusively mistreat his siblings, but he did target them, or at least was shown as the type who would if he had had brothers and sisters. (For example, he might be shown acting like a devil toward the pets, who are surrogate siblings.)
One objection to this line of thinking is that we can reduce it all to how inclined people are to use violence -- the whole of society has gotten a lot less violent in the past 20 years, and less sibling vs. sibling cage matches are just a special case of that. Nah, this is a lot more of a drop than what we see in the violent crime rates -- it's not like little brothers are only 50% less likely to get clothes-lined nowadays, it's like it hardly happens at all.
The decline in violence explains a good deal of the decline in sibling rivalry, but there's a lot more of a drop left unexplained. The main source of sibling rivalry is genetic dissimilarity, so it should ramp up in more promiscuous times, which tend to be more violent times. Taking both of these factors into account, I think we can explain the rest of that mysterious disappearance of sibling rivalry.