From research that I've recently done, there are many younger people, as well as baby-boomers that like the 1961 film West Side Story a great deal, as well. If West Side Story were to be re-made as a more up to-date movie, it would not only be fraught with steamier and more explicitly sexual romantic relationships, but the fights between the Sharks and the Jets would be undoubtedly more graphic and bloodier, the language much "bluer", and the use of guns, rather than fisticuffs and switchblade knives would be present in the rumble, and more people would be killed. In addition, the police, as in real life, would be more militarized, and the musical score would undoubtedly be a cheaper, junkier, schmaltzier form of the original musical score, or a more hip-hop, rap-type version of it.
Having said all of the above, if we wish to unite the baby-boomers and the millennials in their liking of West Side Story and other great classic films, is not by re-making them, but to have more frequent re-releases of such films back into the movie theatres, including both the few independent repertory movie theatres and the multiplex cinemas alike. Having some of these great old classic films, including West Side Story (the 1961 film) would, I believe, undoubtedly draw more people back to the movie theatres, by reducing the amount of rudeness in the form of cellphone use/texting, talking during films and distracting people who've paid good money to come and see them in the movie theatre, plus the fact that many of these good old classic movies, including West Side Story, Lawrence of Arabia and many others, have become available in Hi-Def DVD for movie theatres, as well.
All of the above having been said, I cannot think of a better way to introduce the film West Side Story to today's younger generations, especially because it's such a rare and special classic in itself.