There are no federal laws that address workplace dress codes, but there are laws protecting individuals from religious discrimination. I am not a legal professional, but it appears as though your employer should allow you to wear skirt scrubs unless their reasoning is for safety reasons or legal requirements.
In order to avoid religious discrimination, employers sometimes need to accommodate employees when it comes to dress codes. In order to receive a reasonable accommodation from an employer, the employee must have a sincerely held religious belief and put the employer on notice that the religious belief conflicts with a workplace rule. Both parties then engage each other in an attempt to find a just solution, unless an accommodation would create an undue hardship for the employer. An undue hardship is anything more than a minimal cost.
If your employer refuses to accommodate your religious beliefs, you should contact a lawyer to see if you have a possible lawsuit or you can file a discrimination charge with the U.S. Equal Employment Opportunity Commission. (removed)