The tapping process has nothing to do with religion. The tapping stimulates both brain hemispheres to interact in unison. It gives a signal to the subconscious mind (the right hemisphere) to act on the command.
As far as Christianity is concerned, Jesus Christ used a higher order of healing-a direct mental path into the subconscious and his divine ability of transmutation combined to create miracles. But his miracles were based on his "patient's" faith. How many times is it written "thy faith has made thee whole"?
EFT does not always work, its necessary to find the exact emotional conflict for EFT to work. Jesus's ability to read minds enabled him to zero in on the conflict bringing the patient to forgiveness or repentance in accordance to the patients conscious will and faith.
Christ alludes that sin causes illness as he tells cured people to "go and sin no more".
EFT is seemingly miraculous because we are culturally accustomed to science's faulty inability to cure emotional traumas and many physical illness.
Medical Science is based upon one simple false assumption: that physical illness must have physical causes. Hence the many "miracles" reported by users of EFT can't be explained in the physical realm and seems mysterious or occultist.
Living life with Christian principles will greatly improve you health and internal peace. I'm Christian and I see no conflict between Christianity and EFT.