Agreed, it's a bit stupid even if she isn't a lesbian. If she is then it's just denial.
Well she started out in Country, which is notoriously right-wing and red state and which would be your entire reason for bearding or covering up if so, from a young age.
I don't think all the chaps she's bearded for have been about classic 'bearding'. I think Mayer and Kennedy were probably more image-related/publicity hookups and Gyllenhaal/Lautner/Styles were for more orientation reasons and perhaps a little publicity too. That's my guess.