This cultural wonder puts out 10 influence per territory under the religion's influence, and that's a lot.  Do you have 30 territories under your religion's influence?  That's 300 influence.  Most importantly, being able to use this offensively to convert neighbours' territories to your culture is enormous.  And because trade routes shrink the distance from distant territories to near-adjacent, this Florentine wonder can make it easy to convert huge parts of the globe.

The influence of 10/religious-territory is strong but reasonable if it's being added to your total influence amount, but is overwhelming and dangerous when it's associated with a specific place on the map.  As a potential change, what if it were added to your net influence per turn but didn't come from the wonder tile?  I'm also wondering if spreading the influence out over the territories would be better or worse for an influence snowball.  *thinking emoji*

Oh, yeah it's incredibly broken. Ironically most of the wonders in the early modern are terribly broken too: Machu Pikachu lets you transfer 50% of the Food produced by Machu Picchu's City to all the rest of your cities; Topkapi Palace provides 100%Industry towards any Shared Project (National Projects (space race, ICBMs), Holy Sites, and Cultural Wonders) and if that wasn't enough it gives +5% industry to the city to top it off; basil's cathedral is incredible as well providing +1Faith per District in your empire, acts as a holy site, +20Faith, +20Stability, and a smattering of influence for adjacent districts: basil combined with Angkor Wat of the medieval era to make food from faith and Macchu Pikachu to spread it is nearly overwhelming to think about; the palace of Versailles makes leveraging 20% cheaper and makes its 20% more expensive for everyone else, annoying any other players/ai that attempt a diplo run; the rest are very good as well. The whole of the early modern early is a little much; gunpowder, op wonders, MUGHALS, settlers, and raze resetting with the early modern colony plan. Some of this, i.e. the colony plan and some wonder strength, could be moved down into a rather currently boring medieval era. 

Cheers!

Hold up, Saint Basil's Cathedral is +1 faith per district in your EMPIRE? :O

And yeah, the faith/influence snowballing is still frustrating -- as soon as a territory flips to another religion/culture, it stops sending faith/influence to its neighbours, so as soon as an empire starts to fall to to a larger culture/religion, that empire rapidly loses tools/options/any way to protect itself.  The "Cultural Eradication" civic can stop the culture flip (though I haven't seen an AI try it), if you can earn it, and nothing stops the religious flip.