I'm currently reading Roger Crowley's City of Fortune, which is about the Republic of Venice's rise as a commercial power during the middle ages and into the early modern era.

In it, he details how the Italian maritime republics like Venice, Genoa, Pisa, and Amalfi all sought valuable trading privileges within the empire, as it formed essentially the crossroads between the wealthy, goods-rich lands of the orient and a western world hungry for those goods. The Byzantines would grant these privileges, usually in exchange for military support in the form of auxiliary naval assistance from the republics' substantial fleets.

Part of the privileges entailed the right to establish trade quarters for the republics' merchant citizens in Constantinople itself, and at their largest point, there were at least 10,000 or more Italians (essentially all of whom would have been Catholics) living in the city as permanent residents.

It is unclear what the average Byzantine citizen or noble in Constantinople (I can't speak for the empire as a whole, but the city does offer a fair amount of insight) thought of the average western Christian, whether there was any sort of deep, vitriolic enmity, or just a pacific sense of superiority over what they would have viewed as a sort of misguided heresy. But by all accounts, westerners were tolerated without much incident of violence or persecution, as long as direct military threat from an outside Catholic Christian force was not imminent. The Greeks as a whole were deeply and fiercely resistant to any kind of overtures or demands from the Holy See in Rome to acknowledge its authority or accept communion with the Catholic Church, but they don't seem to have minded the mere presence of the small minority of Catholics in the empire, and the Imperial throne was happy to play power politics by getting in bed with one Catholic state to gain influence against another whenever it could benefit, such as supporting the Italian city-states against one the Byzantines' chief rivals in the west, the Holy Roman Emperor.

At the time of the Fourth Crusade in 1204, there were even a handful of mosques in the city for the small Muslim population in Constantinople, and it is a reasonable assumption that peaceful toleration The Latin crusaders who were besieging the city attacked one of these mosques outside the walls along with its inhabitants, prompting the Byzantine defenders to come to the Muslims' aid and repel the attackers. It does not seem an unreasonable assumption that persecution of religious minorities was not a regular occurrence in life in the capital.