Clerics of any religion do in fact not usually work on a fee for service basis, rather they are supported by more general income sources like tithes/income from church-owned property or investment/donations/state subsidies etc.
But are there exceptions? There are a significant number of fiercely and proudly pro-capitalist clergy, particularly in the US. Is there any church where, when a parishioner says “Pastor, I am deeply troubled. Could we have a talk?” the answer will be on the lines of “Of course, come along to my study. That will be $100/hour, billed in 15-minutes increments.”?
It’s not always easy to separate the allegations from the facts concerning Scientology, but from what I’ve gathered online, most if not all of the services they offer are fee-based.
I think paying the clergy person directly would have negative tax consequences for him or her. I’ve never heard of paying for counselling from a clergyperson, but I could see it for other services like a wedding where the couple does not attend the church. Even then, though, the payment would typically go to the church (with the clergy perhaps receiving a tip or gratuity).
I’ve never heard of clergy charging a fee for pastoral care. I have experienced a minister refusing an honorarium for performing a wedding for non-members.
Charging to minister to church members would probably go over as well as a turd in the punchbowl – I can’t imagine anyone getting away with it in the churches I’m familiar with. As for non-members, the clergy at our church are so busy with their assigned duties I don’t see where they’d have the time to take on clients.
Fees for weddings and speaking engagements (for example, hiring another church’s pastor to do your church’s retreat) are pretty common.
A Presbyterian church I attended had a therapist on staff who billed by the hour (though the therapist used a sliding fee scale so that you paid only what you could afford; the church’s funds covered patients who couldn’t pay). But even there, you could still see the pastor about more general-purpose concerns without any fee. Every pastor I’ve ever known has drawn a line between pastoral counseling and therapy, and felt that both had their place.
As for tax implications - this kind of thing would need to classified property and generally reported as self-employment income, but the implications are not necessarily negative unless you count paying taxes as a negative thing in and of itself.