As a white woman who would never presume to comment on Black women's hair because I cannot have any contextual experience in which to frame any reference, I would say that black men need to shut up about it too. Chris Rock, for example, has a long history of comedy routines about Black women's hair issues.
I admit, I've laughed at some Black women joking about their hair issues, like Sheryl Underwood from The Talk. But, I felt kind of unsettled on her behalf when Sharon Osborne made a joke with her (about her wearing a wig, I think). If I remember correctly, it was in the context of Sharon's use of wigs during her cancer treatments (I'm not certain of that context). Even though Sheryl laughed, I remember thinking, that's not cool.