Racism?
I highly doubt it. I think the manager and staff are simply incompetent and rude. I doubt the manager singled you out because you are a person of color.

I think Target needs to take a serious look at the way their system is set up. They should work to improve it to make sure that coupons are inputted properly in the system. Target should also implement a policy where cashiers (or managers) are empowered to override the system to provide the proper discount when a coupon is not coming up correctly in the system. It just sounds idiotic to say "the computer says this is the way it is so thats how its going to be" when clearly the coupon states something different.

Training would be beneficial to show cashiers how to properly handle coupons, but any sort of customer service training would be ineffective.