If I apply for a position where the employer is required by law to perform background checks, will this affect my rights?

Q & A Main Article 3

Maybe. When a specific law requires a background check, that law usually outlines the rights employees or applicants have as well. These rights may or may not coincide with those you’d have under the Fair Credit Reporting Act (FCRA).

Unlike most private employers, law enforcement agencies and state licensing authorities might have direct access to state and federal criminal records databases. A government-run database isn't subject to the FCRA, but you'll likely be able to find out what your rights are by contacting the agency or looking in any background check form you signed. 

Individuals are generally allowed to access their criminal records maintained by a state or federal agency. To learn how to access your state criminal records, visit your state Attorney General’s website. To check your federal criminal records, contact the Federal Bureau of Investigation.