People should be able to read what they want to read, otherwise they wouldn't be reading much at all.
I enjoyed a lot of YA and juvenile in high school and have loved it ever since. However, I was a creative writing major in college and as such I had to take a number of literature classes. A literature class, for those who don't know, is like a book club on steroids. There's massive amounts of reading and then each piece gets dissected to death in class and you get graded based on how well you can break it down, how much you participate, and how much your professor likes your insightful opinions on it (I'm a little bitter because no matter how hard I tried, I was a solid B student in most lit classes). I saw things pretty differently from a lot of my classmates and I felt like I was one of the few people who didn't look down on YA and other modern "Garbage". These people treated Faulkner and Hemingway like gods and wouldn't be caught dead reading anything with slang in the title. I hated those classes because it made me feel like there was something I wasn't getting - that my simple minded brain couldn't understand the deep meaning in these well respected works. I loved reading and writing, but I could not get behind the way my literature professors were trying to get me to think. I tried to like it - there was a number of things that I did like such as Heart of Darkness by Conrad, which surprised everyone including myself because it's a horrific story and most people hate it. I also love anything by Jane Austen or the Bronte sisters, Shakespeare, some stuff by Socrates, The Prince, and William Carlos Williams. But put John Donne in front of me and I'll promptly fall asleep - I really didn't understand the appeal Donne had for my fellow classmates.
There are some amazing YA novels out there that send strong messages and have beautiful writing and tone. I think a big part of what makes YA appeal to adults as well as teens is the pacing. As a full time worker and student, it's easier for me to read YA for fun that it would be to read a lot of adult novels. I enjoy a lot of adult fiction now that I'm older than most YA protagonists, however, I always come back to YA because not only am I a sucker for some teenage paranormal dystopian/utopian world building and innocent romance but because I want to make sure I relate to my patrons and what they are reading. I work in the children's area so I also find juvenile chapter books I find interesting. I've read half of the Diary of a Wimpy Kid series and still enjoyed it. I also recently read another juvenile book, The Iron Trial by Cassandra Clare and Holly Black and it really brought me back to what it felt like reading Harry Potter for the first time.
I don't think there's anything wrong with adults reading YA or children's novels. Adults are busy and if they are actually taking the time to read it should be something that appeals to them that they can enjoy instead of trying to read something else because they think it's appropriate or good for them because society says so. I believe librarians should encourage adults to read YA if they want to. It can be tough sometimes because teens books are cataloged and shelved separately from adult books and is a shelving/cataloging nightmare to try to put the same book in two different locations. Where I work in particular, we may be unintentionally scaring off adults who want to read YA because I work at a large central library where we need to keep our children's area safe and our security team will kick out any adult who is there without a child. As library staff, we've tried to get security to be a little nicer because we know teachers often come without children to get books. We try to beat the security guards to lone adult patrons and politely ask if they're with kids or are looking for children or teen materials so that way we don't deter an adult from getting a YA book for themselves.
Think about it this way: when a lot of this classic literature was published, people of those times likely thought some of it was garbage too. Jane Austen would probably have been considered a YA author in her time. A hundred years from now students will be studying the Hunger Games and tearing it apart the way students today debate about what Fitzgerald was trying to say with the green light in The Great Gatsby.