To answer your question directly, yes. You can bring the charge of discrimination and continue to work for your employer. It is, however, important to make a distinction between filing a charge of discrimination and filing a lawsuit. Before you can sue the company, you need to timely file a charge of discrimination with the Equal Employment Opportunity Commission. The deadline is 180 days from the wrongful act, but you should contact a California attorney because if California has a local agency handling such claims, the deadline may be extended. Until you talk to a California attorney or the EEOC, assume the deadline is 180 days. Do not miss the deadline or you may lose your ability to pursue the claim. You should know that if you bring a charge of discrimination with the EEOC and the company fires you or takes any adverse action against you because you brought the charge against them, you can bring a separate charge (and a separate suit) for retaliation.
Disclaimer: This answer is provided for informational purposes only, does not constitute legal advice, and does not create an attorney-client relationship. Actual legal advice can only be provided after completing a comprehensive consultation in which all of the relevant facts are discussed and reviewed.
You did not provide enough information to determine whether or not your company discriminated against you, so it would be advisable to consult with a local attorney to give you legal advice, as to answer your question well, would require more specific details. Whether or not your employer can terminate you if you sue them, depends on several factors, including what type of organization you work for, how many employees work for the company, whether it is a private company or public company, union or non-union, and whether you are a contract employee or an "at will" employee. If for example you live in an "at will" state, your employer can terminate you for any reason or no reason at all, as long as the real reason is not discriminatory.
Generally speaking, if you work for a company who employs 15 or more employees, the employer may not retaliate against you for complaining about discrimination or harassment at work, or
for filing a discrimination claim. It is illegal for an employer to terminate a person, to move an employee to a less favorable job or shift, or to give someone a poor evaluation solely on the basis of the employee’s discrimination complaint.
However it would be advisable for you to consult with a local attorney who can discuss the details of your particular situation with you in more detail and give you a more informed answer to your question based off your specific facts.
Yes. In fact, California law protects employees who oppose unlawful conduct in the workplace by providing a cause of action for retaliation. If you want to make a claim for discrimination on the basis of sex and/or race, you should file a claim with the state Department of Fair Employment & Housing (DFEH) immediately. It appears from the limited facts that you provided that you have an indirect evidence case subject to the burden shifting framework for opposing summary judgment laid out in McDonnell Douglas. (McDonnell Douglas Corp. v. Green (1973) 411 U.S. 792.) If your employer, in response to your initial DFEH claim, terminates you or otherwise mistreats you in the terms and conditions of your employment, you can make another DFEH claim for retaliation. You should consult with a California employment attorney. These cases are very fact specific.
Disclaimer: This answer is provided for informational purposes only, does not constitute legal advice, and does not create an attorney-client relationship.