Clones would be just like any "normal" person. Who would treat them differently based purely on the fact that they were clones? The abnormal people of course!
I mean those delusional members of society that would believe that they were somehow special and important for having burst forth from the loins of their parent as, what they believe to be, a unique human. I mean the theists. I mean the Christians.
Most likely we can expect a few wacked out southern baptist sects to deride clones as "souless abominations" much like they've been deriding non-white minorities as lesser humans for the past 25 years.
Gee... I can barely wait...