LGBT-friendly Middle Ages?

Alright, so here's the history of the world I'm thinking of so far:

In 467 AD, the Germanic king Odoacer was killed during a hunt, where he was thrown from his horse accidently and crushed and cracked his head open. The Germanic people of northern Italy lament his death, and do not have a leader with his capabilities again.

480 AD, the Germanic chiefs who lead the various Roman mercenary groups turn against Rome, with multiple other barbarian tribes also migrating across Roman lands. Initially, everything except for Italy is invaded, but eventually the Italian peninsula comes under threat as well.

Italy finally capitulates to the Visigoths under Alaric, who march southwards to Sicily in an attempt to cross the Mediterranean to settle in Africa. However, the Emperor of the Eastern Roman Emperor (now known as the Empire of the Greeks), Emperor Zeno, sends a large Greek force to surround and starve the Visigoths and reclaimed Italy for their own.

With the previous emperor Romulus Augustulus deposed, Zeno gave his kinsman Julius Nepos the Throne of Italy, allowing the Leonid dynasty to rule over both Empires. Julius set about squashing all remnants of the old corrupt order (which was not hard since the old emperor's were blamed for the fall of Rome). Italy was turned into an authoritarian monarchy, and a client state of the Empire of the Greeks.

With the Romans having lost control over most of their empire, they figured that their best chance to exert their authority was to control the religion, so the Roman Church took more authority over the writing of Christian teachings and the bible itself. One important aspect was the openness of sexuality - including tolerance of homosexuality - which was common in Roman culture.

However, during the period 700-900 AD the Empire of the Greeks and the Kingdom of Italy begin to divide over the matters of religion - Italy remained heavily influenced by Roman culture, and were very open with sexuality, whereas their eastern counterparts were by nature more conservative.

This division boiled over in 916 AD with the Council of Constantinople, where the bishops of the east and west discussed religion. After a month of debate they decided to accept Italy's style of Christianity - a move that angered much of the populace in Greece. All over the Empire revolts sprang up, and within a year a new Emperor usurped the throne, one that was far more conservative. This began an era of mass persecution - victims included Jews, homosexuals, heretics and disloyal clergymen.

The atrocities committed in Greece compelled Italy to launch a crusade against them, with most of Western Europe answering their call. By this point in time the religions were:

1: Roman Christianity - Italy, Francia, England, Northern Iberia & Dalmatia.

2: Orthodox Christianity - Greece, Levant, North Africa, Southern Iberia.

3: Paganism - Germany, Scandinavia, Russia etc.

If there's anything that needs to be added I'd be glad to do so - otherwise hopefully this is a satisfying creation of our worldbuilding!