deep, deep-rooted, deep-seated, strong
blatant
serious (esp. BrE), unfair (esp. BrE)
personal
popular
She has not been afraid to challenge popular prejudices.

old
It's hard to break down old prejudices.

blind, irrational
anti-Catholic, anti-gay, etc.
class, colour/color (esp. AmE), cultural, ethnic, political, race (esp. AmE), racial, religious, sexist, social

have, hold
We all have prejudices of some kind.

air, express
He sat there airing his personal prejudices.

appeal to, pander to
We must not pander to the irrational prejudices of a small minority.

confirm, reinforce
encounter
She had never encountered such deep prejudice before.

confront, face
suffer
challenge, fight
overcome, put aside
It's time to put aside our old prejudices.

break down, eliminate, eradicate

without prejudice
The tale is told without prejudice or bias.

prejudice about
a book written to challenge prejudices about disabled people

prejudice against
deep-rooted prejudice against homosexuals

prejudice among
prejudice among ignorant people

prejudice towards/toward
prejudice towards/toward immigrants

a victim of prejudice