Well, I have much to confess about lack of background knowledge: I've managed to never watch a production of Romeo and Juliet of any kind, on screen or stage. I only know the story from summaries, as I'm not the sort of person to read Shakespeare for fun. Nor have I seen the original West Side Story in full - I started watching it once, and thought the finger clicking street dancing was a little silly. Maybe I saw a bit of later dancing, but never watched it all.
So, I come to the Spielberg movie with a moderately clean slate, which leads me to say this - I actually get why it hasn't found a young audience. The musical is a period piece of its day, based on a play with a story that surely must only convince by the poetry of its language rather than the probability of its plot. I mean, I certainly hope Shakespeare does a better job of convincing his audience that the love at first sight of this couple is plausible. (I don't deny that people do say they "knew at first sight", so perhaps I shouldn't be so dismissive, but I have a deep preference for the slow burn romance over the instant "I knew he/she was for me" any day of the week. In fact, let's mention now the deep irony that Robert Wise directed for the screen both WSS and The Sound of Music, the latter featuring the most utterly charming and convincing "falling in love during a dance" sequence that I know of in a movie - the crucial difference being that the second Maria had known this dude by being a part of his household for at least months before the ball. In West Side Story, it's more a case of seeing each across the crowded dance floor, a 60 second dance like a pair of mating birds, and that's it. I know which I find more convincing.)
For me, the musical is flawed in other ways - I thought a key dramatic song A Boy Like That, which I was hearing for the first time, is both musically and lyrically a real dud. In fact, that song is related to the biggest single thing that doesn't help the musical: Bernardo (who is killed by Tony/Romeo) being turned into Maria's brother instead of her cousin, as in the original Shakespeare. Sure, Maria seems to have a tense relationship with him, but she still seems to love him as a brother, making her instant forgiveness (and more!) of Tony much harder to understand.
OK, so I am full of criticisms - but despite all of this, the movie infected my dreams in the way that a good movie does - and all because it is exquisitely directed.
The dance numbers in particular - as I wrote before, I knew from as early as 1941 that he should be able to do them well, and honestly, the amount of pleasure I got from the way any dancing is directed and editted in this film was pretty immense.
So, it makes for a weird conflict in terms of recommending the film - I completely understand if you don't think it's a good musical, that it has a silly story, and even the actor playing Tony being the weakest of the stars (the women are uniformly terrific, and the other male leads really good too - and obviously ridiculously talented) - but you should see it anyway and be in awe of how it is put together. If you're lucky, it will give you some nice musical dreams afterwards, too.
On some end notes: the movie is remarkable for attracting highly political partisan commentary from both the nutty, Trumpian Right ("it's too Woke!") and the identity politics obsessed part of the Left ("it still trades on racial stereotypes - this musical should be forgotten!"). I think the attempts to drag it into more modern relevance were quite OK - and I find it hard to fault Spielberg and Krushner's liberal, inclusive, instincts. I thought occasionally that the lack of subtitle for some Spanish was a bit harmful to understanding, but as an artistic decision, I basically have no problem with it. The lack of youth appeal, as I said above, goes back to the faults in the musical itself. Oh, and young women (like my daughter) wanting vengeance on Ansel Elgort for sexting a girl while he had a girlfriend.)
The politics of Leonard Bernstein, and of America post WW2, were the subject of a very interesting article at Slate last month, and I strongly recommend reading it to give context to the musical.
Update: I watched this lengthy discussion of the two movies last night, and it goes into a lot of interesting history of the musical itself, how Hollywood treated stars who couldn't sing well enough, and casting decisions. (The bit about Natalie Wood being lied to as long as possible that her recorded songs were going to be used was pretty amazing.) All very interesting: