I know that in the earlier history of the church, it was not a requirement, and that certain monasteries were mixed-gender, and was wondering when this started.
I was also wondering if the works of St. Justinian had anything to do with this decision?
This is not my particular area of expertise (hopefully a medieval specialist can jump in for more clarity), but this tradition of priests being forbidden from marrying started with the First Council of the Lateran in 1123 CE under Pope Calixtus II. Here, members of major religious orders were banned from marrying. Within two decades, another council was called under Pope Innocent II called the Second Council of the Lateran, in 1139 CE. Here, it was firmly established that all members of the clergy were forbidden to have marriages or concubines. A transcript of the orders can be found here
What's interesting in it, is that those whom were already married were supposed to dissolve their marriages and any priest who failed to do so had his congregation forbidden from attending his services. Canon 7 from the council decreed:
Following in the footsteps of our predecessors, the Roman pontiff s Gregory VII, Urban, and Paschal, we command that no one attend the masses of those who are known to have wives or concubines.
It was clear that the church wanted (maybe even needed) to regain complete control over its clergy, and by controlling marriage (and the ability to have children) this empowered the church to have a tighter grip over it's men.
On the topic of St Justinian, The Emperor, I am sorry to say that I know incredibly little about him, so I don't really have much of an opinion about this that would be credible.
Hope this helped a little