Not a professional historian, and the question is incredibly broad (almost 1500 years of history), but I’ll point a couple things that are often on my mind.

The Eastern Roman Empire eventually imported and developed an extreme culture of the “eunuch court.” Basically educated men who were castrated either as children or as some sort of punishment would compose a very large portion of the Emperor’s entourage, and handled all sorts of administrative tasks that before were handled by young men of equestrian or senatorial rank.

This was done in part due to their weird Christian views that the Emperor was the representative of God, so no imperfect man could expect to do a coup from within that position, but also because their extreme sexism made them incapable of believing that a woman could fulfil those functions. If you read the biography of some prominent Eastern Roman, it’s likely that you’ll read the word “castrated” a couple times.

It got so ingrained into their culture that castration or blinding became common punishment for men of high ranking families who sought to overthrow their superiors, and the first Empress Regnant, Irene of Athens, blinded her own son after he tried a coup on her. It is possible that she also tried to marry Charlemagne and reunify the empire that way, which makes for some cool alternate history.

Another fun bit is that, at least for the early pagan Romans, adoption had a very different connotation than it has to us today. Basically, an older Roman citizen, often a patrician, would adopt a grown man of lower status into their family regardless of whether they even still had biological parents. This new “son” would then inherit the family name (Gaius Octavius -> Gaius Julius Caesar Octavianus), and effectively become an heir, but they wouldn’t be expected to have the familial affection and cultural aspects of today. In fact, it was very common for men to adopt their younger male lovers. Augustus even adopted his own wife posthumously.

They also repeated names a lot, specially for women who effectively had no names of their own for the most part. Look at this family tree and despair.

As a final major one, the Bishopric of Rome was never the supreme representative of the Christian faith within the Roman Empire, being dedicated to administrating only with Western Europe within the Pentarchy system. The actual representative of God was the Emperor himself (no idea how that works when there are like 6 of them warring about), and the “first among equals” of the bishops was the Patriarch of Constantinople. This whole notion of the “Roman” “Catholic” Church being the supreme leader of Christianity comes from a forged document called the “Donation of Constantine” that supposedly transferred all Roman authority in the west to the Bishop of Rome (now Pope), which got peddled around a lot during the development of the East-West Schism crisis, specially after the establishment of the “Holy” “Roman” Empire.

After the empire finally fell for good in 1453, there was a mass “pillaging” of their titles, with a bunch of kings claiming to be the actual successor, but notably here the Papacy also borrowed the ancient Roman title “Pontifex Maximus” and put it in a lot of their official stuff.

And this rift between the Western and Eastern churches only got properly addressed during Vatican II in the 60s, possibly due to some Cold War shenanigans.

Also, of the 5 known as the “Five Good Emperors,” 3 of them really enjoyed men’s company. And since I’m already here, some Roman writings called the Britons “Brittunculli”. I wish that one could catch on again.