If this were a place where the Church had strong influence, Hudson would not dare engage in such a heretical act. However, this was the Alpha Kingdom, a place where a priest had to submit to the preferences of the nobility.
The priests in the domains might be dissatisfied, but they would absolutely not dare create chaos. Even if they aren't willing to comply, the clans behind them would force them to behave.
Only the High Priest is qualified to have a say. In Hudson's domain, there were only a group of low-ranking priests.
If they didn't want to do it, there were plenty of people outside waiting to take their place. Catering to the medical needs of the nobility didn't require a huge number of people.
Furthermore, even though this kind of change would challenge the status of priests, its overall impact would be minimal.
The declining pharmacists, even if they revived in the mountain domain, could only provide medical services to serfs for a long period in the future.