I think that there is some misunderstanding about Mercenaries. As one who has studied them most his life, written papers on them (and even wanted to be one), I can tell you this: being a mercenary simply means that you are doing something just for pay. The earliest Mercenaries would fight for the highest bidder, often changing clients as the winds of fate blew. That is one of the things that gave the term "mercenary" a less than honorable connotation. However, not all Mercenaries were without honor. The French Foreign Legion is one of the more honorable mercenary organizations throughout history.
How does this apply to religion? We are supposed to do good because it is good, not just for reward. Too often we do good because there is a return on the action, be it financial or otherwise. An example would be one that gives openly to the Church, and with great fanfare. The scriptures tell us that the left hand should not know what the right hand is doing, and that what is done for God in secret is seen by God. The "Un-mercenary Healers" were such because they healed for the glory of God, and not for their own gain or fame. Modern doctors can be either mercenary or un-mercenary. There are some that actually care for their patients and become doctors to ease the suffering of man. The fact that they are compensated for their work does not make them mercenaries. Many give hours of their time for little to no charge. On the other hand, I have known doctors for whom a patient was just another payment on his Lexus. These would be mercenaries even if they made less than the former doctors.
Being a mercenary is not always bad. For example, in my work I am very mercenary. I work for the highest bidder and have little loyalty to an employer. I have seen first hand their loyalty to me and to other workers (rather, the lack thereof). My employment is strictly business, and if my pay stops my work for that particular employer also stops. I do not consider this form of mercenary activity to be dishonest or unholy. Certainly not dishonest because I used to keep a sign on my desk that said "People work for money. If you want loyalty, buy a dog." On the other hand, my work with the Church is quite different. Given that I have a high paying secular job, I cannot in clear conscience take any compensation for my work with the Church. In fact, I don't even like to get paid for my expenses. My Church work is, by my standards, un-mercenary. In fact, given the dismal way that most Orthodox Churches pay their priests, my guess is that most paid priests and deacons are un-mercenary. Televangelists, on the other hand, seem to me to be the ultimate religious mercenary. But, I may be wrong since I do not know for sure what is in their hearts.
One must also be careful about volunteer work. On the surface, the fact that it is volunteer would seem to make it un-mercenary. However, if you are doing it just for the praise and recognition, they you are doing it for gain and not because it is good. So, the prayer to guard us against mercenary actions is more complex than the simple definition of a mercenary. One can be a mercenary and not receive one red cent for his work.