A Christian servant will behave according to the norms of the church and his religion, theoretically he must maintain ethical, respectful and in accordance with the bible.
In this sense, a Christian servant and a non-Christian servant have extremely different behaviors, they are people who think and behave in different ways.
I believe that God's servants can apply to different religions, but since each religion sees God in a way, I don't believe that only one way of being a slave can supply all religions.