Brooklyn Shooting Victim -- Rev. Al Sharpton Pulls Out of Funeral Due to Family Rift

Rev. Al Sharpton is bailing on delivering the eulogy at services for the Brooklyn man who was gunned down by NYPD -- and he says it's because he's caught in the middle of a family battle.

As TMZ first reported ... Akai Gurley's mother and aunt had demanded Sharpton stay away from Friday night's wake and today's funeral. His aunt claims the Rev. is making a circus out of the tragedy.

Gurley was shot and killed by a cop in a Brooklyn housing project stairwell. There's been outrage over the case because the cop who shot him allegedly texted his union rep before calling 911.

Sharpton say he's been working with Kimberly Ballinger ... Akai's domestic partner and mother of his child at her request -- but late Friday he decided he would skip the services due to "confusion and division" amongst Gurley's family members.

Further, Rev. Sharpton says claims by Gurley's aunt that he's grandstanding for money ... are unfounded. He tells TMZ he has never asked Ballinger, or any other family member for money -- and would have no reason to do so, since his TV contracts keep him flush.