In order to invoke federal jurisdiction they have to show that there is probable cause that the shooting was motivated by federally protected conduct. What would that be?
That is not correct. The relevant clause of the statute - the one the feds will use to get him - has nothing to do with motivation. It's very straightforward =>
Whoever, under color of any law, statute, ordinance, regulation, or custom, willfully subjects any person in any State, Territory, Commonwealth, Possession, or District to the deprivation of any rights, privileges, or immunities secured or protected by the Constitution or laws of the United States,...