Employees in a restaurant can and should be required to dress a certain way. This may be both in terms of hygiene and brand recognition.
Employers have the right to require certain dress for employees.
For employees in the private sector, the right to dress their own way is quite limited, and a right to privacy is almost non-existent when it comes to dress code enforcement. (bizjournals.com)
However, an employer needs to make sure the dress code is specific. For example, if everyone should have a shirt tucked in, then this should be in the dress code. Some dress codes specify the color or type of shoes, and some even require a certain color or type of socks. The dress code should be as specific as possible.
It may be worn outside or tucked in. If you wear an undershirt, it must be white. No long sleeves. (klondikepizza.com)
Sometimes an employee’s uniform is provided, and in that case the specific uniform elements need to be in the dress code. For example, if you do not provide shoes you need to specify the type of shoes.
Dress code also includes things like hair length, hair style, and piercing. One exception to the law the employers can require anything is religion.
Employees who must wear certain clothing because of their religion may also have some protection. (bizjournals.com)
Employers should make sure they are respectful of employee religions in the dress code.