While one could bring such a lawsuit, the more important question really is, is such a lawsuit winnable? Public employees are not a protected class under the federal discrimination laws, so a lawsuit brought claiming discrimination on the basis of being a public employee not allowed to arbitrate most likely would fail. Unless one can find a federal statutory allowance for bringing such a lawsuit then such a lawsuit likely would not get off the ground. I am not aware of any such statutory allowance.
Disclaimer Information on this site is provided by Brian Scott Wayson as general information, not legal advice, and use of this information does not establish an attorney-client relationship. If you have questions about your specific situation, please call an attorney.
It seems unlikely. By "discrimination against public employees" who are not police officers or firefighters, you may be asking if there is a denial of Equal Protection under the 14th Amendment. The government would have a sufficient rational basis to treat police and firefighers differently than all other public employees in general.
As a "public employee" in general, you don't specified if you are tenured. Some government employees would have no tenure, or property interest in their job to begin with. Further police and firefighters who have arbitration as a remedy may be precluded from pursuing a remedy in Court, so there is a tradeoff, justifying the distinction.
I agree with the first two answers, such a lawsuit is very unlikely to result in a favorable verdict. You are not in a protected class and the court is unlikely to see a Federal issue.