Your post doesn't give a lot of details such as why a credit report would be necessary for your particular job and why it would get you fired. An employer must limit their background checks to what is relevant to the job not get info forany all personal information. I say contact a lawyer. Here is some info from the web:
Credit reports. Under the Fair Credit Reporting Act, or FCRA (15 U.S.C. §1681), employers must get an employee's written consent before seeking that employee's credit report. Many employers routinely include a request for such consent in their employment applications. If you decide not to hire or promote someone based on information in the credit report, you must provide a copy of the report and let the applicant know of his or her right to challenge the report under the FCRA. Some states have more stringent rules limiting the use of credit reports.
Try and check you state laws on privacy, background checks laws. Good luck!