Thank you for the additional information, Gianni.
Yes, as part of the employer's dress code, they can typically insist that female employees wear bras, and that would not typically violate any state or federal laws.
Sex discrimination claims typically are not successful unless the dress policy has no basis in social customs, differentiates significantly between men and women, or imposes a greater burden on women. Thus, a policy that requires female managers to wear uniforms while male managers are allowed to wear "professional dress" may be discriminatory. However, dress requirements that reflect current social norms generally are upheld, even when they affect only one sex. For example, in a decision by the Eleventh Circuit Court of Appeals in Harper v. Blockbuster Entertainment Corp., 139 F.3d 1385 (11th Cir. 1998), the court upheld an employer’s policy that required only male employees to cut their long hair.
Here is a link that provides more information on this issue as to wear the courts draw the line with regard to implementing and enforcing dress codes:
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