What if I’m Christian but I believe in reincarnation? 

In Jesus's day reincarnation was such a naturally accepted concept that it did not require discussion. The New Testament contains a little gem that proves that reincarnation was acceptable even to Jesus who did not condemn it. After He had healed the man born blind from birth He was asked by His Disciples about the type sin the man or his parents had committed that resulted in him being born blind. Jesus did not condemn the concept but explained that in this particular case it was not because of any sin but had been planned that way for the purpose of "glorifying the Son of Man" - in other words demonstrating Jesus's powers over physical afflictions.

There is a great story of a young boy, 9/11 and the reincarnation of a New York City fire lieutenant who perished in The North Tower. The full story as told by the boy's mother on (and off) a popular Reincarnation Forum starting in 2007 up to the present day. The books full title, Fire in the Soul: Reincarnation from Antietam to Ground Zero. The author is Jeffrey Keene a retired Asst. Fire Chief.

His quote doesn't even disprove reincarnation. In reincarnation, you die once as a man and then you get judged before you move on to your next life.

The bible talks of rebirth. the exact Greek noun "rebirth" or "regeneration" (Ancient Greek: παλιγγενεσία, romanized: palingenesia) New Testament (Matthew 19:28 and Titus 3:5), regeneration represents a wider theme of re-creation and spiritual rebirth.