I guess it just seems obvious to me that we should encourage and promote the reading of YA literature and graphic novels by adults, or reading of any kind really. As a public library, we have no right to determine what is or is not appropriate, especially for grown adults. We promote and protect the freedom to read. Furthermore, many of these YA books are considered "crossovers" because they appeal to more than one audience. Their subject matter goes further than teeny bopper love story (which is also fine if that's what you like to read). Graphic novels can definitely be more than comics; Watchmen is considered one of the greatest novels ever written.
With that being said, there are several things that can be done to ensure we are serving adults, such as myself, who enjoy YA literature and graphic novels. We can continue to promote these materials through displays and booklists. I created a list a few weeks back for my special topics paper that has YA books that will appeal to adults as well as teens. Librarians can also offer book discussions geared towards adults that discuss young adult works or graphic novels.
One of the most important things we can do because there is such a stigma towards reading these books is making sure that we have an excellent selection available online. This included ebooks and e-audiobooks. If people are embarrassed of showing the cover, as we saw in the case of romance books, ebooks allow them to keep their reading selection private. Along these same lines, librarians can offer online book discussions so that people can still share about their books but in the privacy of their own homes.