It is customary to pay a minister for performing a wedding for you.
Some charge an established fee, others are just voluntarily given honoraria by the marrying couple. (this is probably the most common situation here in the U.S.)
Some Churches have a policy that non-members pay x, members may give as they see fit. Others charge non-members more than members. Others charge the same to everyone (rare, since members are already giving stewardship throughout the year). Some Churches do not marry non-members at all.
As the Scriptures say, a worker deserves his wages (1Tim 5:18
http://biblehub.com/1_timothy/5-18.htm) It is *right* to pay a Clergyman for a wedding.
Some folks have a tie to a certain Church, but are not active members (Grandma goes to this Church, and I always went there when I was a kid, or I am a Baptist, but far from my home Church, and this is a *pretty* Baptist Church). Or, I am a Catholic, and I must marry in a Catholic Church, but my hometown is far away. There are lots of reasons to get married in a Church you don't know. I was married in DH's Childhood Church - we have strong ties there, but are not active members. For many Christians, a wedding MUST be done in a Church to be "Christian" others believe that it only must be done by a Pastor (in contrast to a Justice of the Peace)
In no case do Churches marry those who they think should not marry. For instance, the vast majority of Churches will not marry a Christian with a non-Christian.