As I see it, these things are determined by the social norms of the culture more broadly, rather than that of the religions per se. The typical model of Western nations is that people are paid for their services. Serving as clergy in a professional capacity is of course a service, and as such, should be monetarily compensated.
There's also a long history in Christianity of explicitly not paying for religious "services:"
Simony - Wikipedia
Catholicism considers simony a sin. It was also a major issue in the Protestant Reformation, so many Protestant denominations have a long tradition against the practice as well.
It can make for weird arrangements involving churches and money. I remember arranging my first wedding (in a Catholic church) - the priest was very careful to clarify that the mandatory fees were just for the organist and decorations, and the "suggested donation" for the wedding ceremony itself was voluntary and that they were
definitely not charging money to perform a sacrament.
... though he also made it clear that
most people pay the suggested donation.