I'm not an expert but from my understanding much of the Renaissance involved the rediscovery and idolozation of ancient artwork and culture by the noble class. I'm going off knowledge of Lorenzo De Medici (late 15th century) in particular but from what I've read it sounds like many wealthy families would collect/show off ancient art and literature. To be cultured in this time meant being versed in this art and literature from the ancient world. This base fueled the commissioning of tons of new art and many artists of the time likewise looked at these examples from antiquity to model their works after. Lorenzo was famous for having a garden where this art was on display and his young sponsored artisans would spend their days studying it. I believe he was also never too fond of catholic teaching preferring instead the ancient writers and thinkers, his wife from Rome on the other hand was much more devout.

Regarding how this plays into the church, I'd say quite simply that many higher ranking church members were from wealthy families. The church was a huge political player on the Italian peninsula, not mentioning Europe, so much attention and pride was place in securing family members in high ranking church postings. These individuals likely grew up with some level of respect or admiration of the ancient arts and lore based on the culture of the times. Again returning to Lorenzo, you have his son rising to the level of Pope. And sure enough he was known for excessive spending on art and other fanciful endevours. Having grown up in the Medici household it's easy to see he likely had less qualms about representing pagan dieties as it simply harkoned back to the classical art of ancient Rome or Greece which was held in high regard. (I have no direct source of Leo X commissioning pagan art but hope instead to draw the connection here in how the wealthy and powerful, raised in a culture of classical admiration, could likely look past strict religious lines while commissioning art).

In fact, this was also the time in which the reformation figures were rising to prominence due to the corruption of the Catholic Church. It's probably fair to say, though speculation on my part, that along with the copious amounts of spending, gaudiness and downright shady dealings promoted by the Pope and church, these hypocricies of idolozation could likely have been pieces fueling the growing contempt for catholicism. Savonarola also came to prominence as a devout crusader against all of the art and literature of this time he deemed to be sacrilegious.

It was very much a time where catholic church officials can be argued to be very far off base with catholic teachings and morals in general. Hence the above revolts on the church.

Tldr: It's a by-product of the Renaissance trend of idolization of ancient arts and literature in the elite class coupled with the church being used more for power jockeying by the elites rather than a place for the devout to rise up the ranks.

Main source: 'Magnifico' by Miles Unger