We have those here too, but it's about things like "we have the right to fire you if it turns out you're a Holocaust denier" or "if you're going to complain on Facebook about how awful your job it is, make sure your posts aren't public."Sadly, in America, it is believed the employee will serve as a representative of sorts, and employees will not engage in behaviors that would "bring shame to the company." (Taken from a couple employee handbooks I've had).
Any company that took the position that an employee brought "shame" to the company by having a same-sex partner, coming out as trans, having a child out of wedlock, etc. would likely find themselves on the nasty end of a Human Rights Tribunal decision.