I was thinking about this:
[ID: gif from BBC Sherlock. In their flat at 221b, Sherlock is telling John: "No, I prefer my doctors clean-shaven"). END ID]
During the Victorian Era, having facial hair was a symbol of masculinity. As we well know, in ACD canon (so as in TAB) John had moustaches, while Sherlock didn't have any type of facial hair.
In the series, John grew the moustaches after having met Mary; he didn't wear them in MHR, that is set when he already had met Mary (in his blog he only says "someone" and it's probably her since he's going to propose one month later). He wore moustaches when he told Mrs. Hudson that he had moved on and when he proposed to Mary in TEH (so when their relationship is going to become official and lasting) but, after Sherlock's return and his comments about the moustaches, John decided to shave it.
So, if facial hair stands for masculinity (which in the Victorian Era also meant being straight and living according to certain standards, among which the aesthetic ones) when Sherlock says that he prefers John without moustaches, it means that he prefers John when he doesn't conform to heteronormativity and people's expectations. On the other hand, John wanting to shave when Sherlock returns in his life means that he wants to be his true self now that Sherlock is with him, even if it's very difficult for him, as we well know (here are some thoughts and metas about John's past and traumas and how they led him to repress his bisexuality -> x, x, x - in addition, there's also this interesting meta about Mary being the personification of heteronormativity)
The same concept applies to Sherlock's choice of not wearing the hat; as this meta says, the moustaches and the hat are what the public expects from them but, as I explained before, I think that not only Sherlock's hat but also John's moustaches are a symbol of a public fake image in which they're straight, because that is, in John's opinion, what people except from them.
Facial hair = symbol of masculinity during the Victorian Age
John grew the moustaches when he decided to move on from Sherlock and to propose to Mary
Sherlock prefers John clean-shaven (which means that he prefers when John doesn't force himself to conform to heteronormativity)
Sherlock's hat and John's moustaches are what people expect from them and they represent heterosexuality.
