how did italian artists of the 15th and 16th centuries respond to the "tastes" of their patrons?

Answer 1

They were basically working on demand and very rarely under a real 'inspiration'. Their main goal was to get money from their 'works of art'. Mostly of the artists were receiving idea of what to do direct from their patrons and then it was normal for them that paintings or whatever else were responding to their patrons tastes. Last but not least patrons were choosing the artists based on their previous works or following the 'fashion' of the moment and they were perfectly aware of how the artist was working.

Answer 2

they painted what they felt would pay the most lira, or in case of the church, the most salvalation.

Sort of like what Playboy does with an airbrush prior to publication of the playmate.