Yes, if you refuse to work with a sex offender hired by your employer, you can be fired. (Note: if you do not have an employment contract, you are an employee at will and can be fired at any time, for any reason whatsoever.)Moreover, you could be fired for cause, since your refusal to do the work your employer asks you to do--or to work with the person or coworker it directs you to work with--is both insubordination and a refusal to follow your employers clear directions. Therefore, if you are fired for this reason, you could be denied unemployment compensation or insurance, since someone fired for cause is ineligible for it.