There are special mechanisms that permit certain DNAs to still function within the Barr Bodies. I'll share this article with you as a quick Google search: https://phys.org/news/2016-07-scientists-untangle-barr-body-inactive.html

Learned about how BBs are not silent while chatting with a professor in 2006. I suspect we don't know the exact details just yet, but could do a proper literature search. (Note: expertise is structural biology/biophysics. Almost went into epigenetics instead.)