Yes, an employee who is in a protected class can often still be terminated from their position, but doing so can be a bit more complex for the employer.
As an employer, you know that employees have certain protections against wrongful termination. For instance, Title VII of the Civil Rights Act of 1964 establishes a number of protected classes. These include national origin, sex, religion, color and race.
What this means is that you cannot terminate an employee specifically because of their inclusion in one of these classes. If an employee converted to a new religion and you decided to fire them in response, for example, it would be a clear violation of their rights.
But you can still fire them for other reasons, such as performance issues on the job, even if they are in a protected class. You just cannot use that protected characteristic as the reason for the termination, as doing so would be discriminatory.
Documenting everything
If you do need to fire an employee in a protected class, it can be very important to gather documentation. This can support your decision and show your reasoning. Examples could include warnings the employee was given or write-ups they received. If you have a clear paper trail showing that there was a valid reason to terminate the employment and that it had nothing to do with personal characteristics, you reduce the chances of a wrongful termination lawsuit.
That being said, these types of conflicts between employers and employees are common, and those involved must know what legal options they have to address them.