The Supreme Court has already ruled that the 11th Amendment does NOT trump the 14th Amendment.
If they step outside their job duties they're vulnerable in their private capacity. The way the game works though is if there's plausible deniability you can't prove motive but that's a game you can win if a thousand people say the same thing about one judge.
Immunity - Whom not to sue in Federal Courts? (This is what I have understood. Please correct me if my understanding is incorrect)
(1) State govt and its agencies have absolute immunity under Eleventh Amendment - Your case will get dismissed
(2) Lawsuit against an employee of State or State agency in their Official capacity - This is considered to be lawsuit against State and they get absolute immunity under Eleventh Amendment - Your case will get dismissed
(3) Lawsuit against State Employees in Individual capacities - They still have Qualified Immunity. In order to attack this qualified immunity, you have to allege that they violated your constitutional rights and they knew that their actions were violating your rights and continued to do so. - Your case can proceed if you have alleged and proved these two things
(4) Lawsuit against County and County Officials - Not sure about this. I think they may have qualified immunity and you may need to legally pierce this supposed immunity.
(5) Lawsuit against employees of Private Companies working for State - They do not get Qualified Immunity as they are not State Actors - Your case can proceed but your allegations still need to be strong.