There is no simple answer for this question however there is one thing I can say for sure is that, if you are able to prove that you are a victim of Racial discrimination then you can sue (file a lawsuit) against that company and get your job plus compensation. Law for racism are very strict and you will always get justice in courts so you need not to worry about racial discrimination.
There are times when a person feels that he is a victim of racial discrimination but he cannot prove it, they might only feel this way. People feel racism in job in fields where there is competition between native Americans and people from other countries. If you are a Citizen or Permanent resident (green card), you will be preferred over others (with work permit & non-resident status) as employment of a permanent resident is more important to the government of United States than of the others.
There are jobs where communication skills plays an important role like Marketing, sales, customer services etc. If we are born and raised in United States then we will have similar communication skills than of the other Americans however if we are an immigrant and does not have a local United States accent with good English then we might not get jobs where communication plays an important role. Even if we are a fluent speaker still the way of communication has a very clear difference and people in United States might not like the way we communicate with others.
Americans do not intentionally discriminate the employees (There might be some who do however I never saw any) however if they feel this person does not posses the qualities that are required for the job, they will not hire you.
Be positive, think positive and strive for the best. You will never get disappointed. Cheers