That too comes with the territory of choosing to alter one's appearance. If the owner of the apartment complex chooses to put forth a professional or upscale community feeling, he would not want to have large tattoos, heavy piercings and blue hair running around the complex. Old people and conservative people, business professional people, if these are his "target customer base" that appearance would scare them off.
It's the same as applying for a job at a bank or a corporate office of any business. A "dress code" is applied and it's perfectly legal, it is not discrimination. If you are unable, or don't wish to, comply with the requirement, you don't apply for the job.
The only problem I had, maybe, with this story, when I heard it yesterday was the question of "Did the office make the appearance requirements completely clear to the couple at the outset?" But that is an unknown unfortunately.