"This is hardly surprising..."
Intrinsically, royal power and divine power have their natural divergences.
It's quite normal for the Medici Family not to put all their eggs in one spiritual basket, so to speak, or in other words, it's a ruler's instinct.
As for why they do not worship new gods like the Spirit Church or the Church of Destiny but instead sacrifice to the already deceased ancient gods?
"The new gods mostly disregard the mortal realm and rarely respond to prayers... whereas the ancient gods, although bloody and insane, if offered sufficiently blood-rich and attention-catching sacrifices, have a higher likelihood of responding..."
"As for the problem of the ancient gods having possibly abdicated or already being dead..."