Should DOD employees be able to have any hair color?

Did her hair color affect her ability to perform the required task to standard?
Or did her hair color affect YOUR ability to perform to standard?

Sounds like none of the first and a little of the second.
Unless the employment offer included a set grooming standard and she is in violation of set standard, hair color, or style has no effect or basis for job performance.

Get over it. Worry about things that affect PERFORMANCE and mission completion.

Employees are expected to comply with reasonable dress and grooming standards based on comfort, productivity, health, safety, and type of position occupied. When clothing such as coats and ties create discomfort during hot weather and in places where cooling is minimized to conserve energy, the requirements should be modified or eliminated.

Any management requirement for specific civilian dress and appearance must be based on a clear showing that the prohibited dress contributes to an unsafe, unhealthy, nonproductive, or disruptive work environment. Management disagreements with styles, modes of dress, and grooming now in fashion is not an adequate criterion for making such a determination.

Employees who wear standard uniforms (guards, firefighters, etc.) may be expected to comply with grooming and appearance standards that are more stringent than those required of other employees. These standards must be in line with job requirements and with like standards for employees in similar occupations employed by other Federal, state, or municipal governments.

Any attempt to dictate appropriate work attire will probaly end up in a lawsuit (especially of the EEO type if a male specifies what is appropriate for a female and vice versa). Most federal workplaces have no official guidance on appropriate dress, only suggestions such as "business attire," or "business casual."

Much also depends where you work and the kind of work you do. Someone who works in printing, graphics, labor - may wear jeans and blue collar type of work clothes. What is unfortunate that many younger employees seem to have no concept of "business casual" (acceptable in nearly every office setting).

And anything dealing with 'enforcing some dress code' has to go thru the labor relations board anyways. Be careful what you say about an federal employee, you might be getting a phone call from EEOC.

SSG (Join to see) The argument you make is similar to the argument made against tattoos. Service members can dye their hair and have tattoos. The limits are in AR 670-1, but I could have a different natural hair color every week.
DoD Civilians are not in the military, they don't represent the military, they do have grooming standards, but they are not the same as ours.
I do not think dyed hair or tattoos are unprofessional. As long as you can wear your proper work attire, for whatever your job is you are fine by me.