American Idiot.
I don’t think there’s a single answer to this question, but I’m sure there’s at least one show out there that most people would like enough to consider seeing at least one more show after.
I have a soft spot for Les Misérables and Notre Dame de Paris. I go down YouTube rabbit holes with those two. “Il est venu le temps des cathédrales…”
Porgy and Bess. Or Showboat.
The music is as good, or better, than anything else, and the stories have more depth. I think they age better than some of the other stuff: they were both retro at the time of writing.
I wouldn’t start with Pinafore except in a small theatre and you have good hearing. The words are hard to follow in a large theatre where you can’t see the faces and separate the singers. If you want something lighter than Showboat, I liked Brigadoon and Music Man: I’m music-driven in my choice of theatre, and I think those two hold up better than later works.
The Music Man is my all-time favorite musical, though I wonder how accessible it’d feel to a younger person, who isn’t familiar with a style of music that’s now over 60 years old. But, the music and story are fun.
I agree that there’s probably no one musical that “everyone likes,” as per the OP’s question. But, another good, fun, accessible-feeling musical (and one of my favorites), which hasn’t been suggested yet, is Joseph and the Amazing Technicolor Dreamcoat. The songs are great, and in a variety of styles, including an Elvis send-up (“Song of the King”) and a song in a French cabaret style (“Those Canaan Days”).
I got to see Donny Osmond play Joseph on stage here in Chicago, around 1994, and he was awesome. There’s a video version of the musical, with Osmond, that appears to be on Amazon Prime.
Those are two of my favorites for light entertainment, but both are so much rooted to a specific setting that someone who doesn’t like rural America or 1940s New York City may get turned off before they even get through the opening number.
On the other hand, if you don’t want to be bogged down by a story line, Anything Goes is a high-energy string of song and dance. The plot is pretty thin, but it doesn’t matter.
For something with a little more contemporary attitude, I’d go with Hairspray.
I’d like to put forth Into the Woods. The folktales context has always seemed easy to reach for my middle school nephews. It is a little slow after intermission but at least reachable.
1776 Great songs and costumes, and easy to follow dumbed down History.
I love Guys and Dolls, but it may not be a great introduction to stage musicals. There’s a lot of dialogue that may not make much sense to many, even through the Runyonesque dialect. Especially to non-gamblers, with the references to horse racing and a floating crap game. The first time I saw the movie, I was peppering my parents with all kinds of questions, and basically forgot the plot, I had so many questions.
I’d suggest Hairspray. The story is easy to understand, and progresses in a linear fashion that makes sense. The songs are catchy and fun, and will likely have most of the audience tapping their feet. If the troupe is good, it will be clear that the cast is having a blast, and that can be infectious.
Another I’d suggest is Little Shop of Horrors. The “horror” part is played strictly for laughs, but the songs are great, especially with Crystal, Ronette, and Chiffon providing a kind of Greek chorus in between scenes, and backing up the leads at times.
All fun till the end… IIRC Audrey-II and offspring conquer the planet. 
Matilda: The Musical had great songs and amazing choreography and stage design.
Sure, but even then it is “fun horror.” I saw the stage version in London in about 1985, and at the end, the audience screamed—then laughed. Heck, I was in a community theatre production of Little Shop some years ago, and we achieved the same.
At any rate, it is not bleak or depressing. It’s a fun one, that makes you leave the theatre laughing and humming the songs.
It’s nice as a solo but for me “Fugue for Tinhorns” (aka “Can Do”) sets the mood for the show and features, as the title says, three intertwining sets of lyrics.
That is a difficult piece of music to sing, and I say that as one who appeared as Benny Southstreet in a community theatre production. Everything has to be right bang on, on time, and in key. Even though the Guys make it sound like they’re not singing at all, they really are (trust me on this). Three males singing tenor, baritone, and bass isn’t easy!
I love musicals.
Moulin Rouge I can drop into at any point and enjoy it.
Phantom of the Opera ditto.
There is always Tommy if it can be found.
The first musical I saw in a real theater was You’re a Good Man, Charlie Brown. It’s pretty much a bunch of the comic strips come to life with songs added. I loved it. I wanted to be Lucy! Even the high school production I saw some decades later was pretty good.
OK, maybe too much nostalgia on my part, but it still gets my vote.
Going back to the OP:
You said they were jaded about live theater. That suggests they used to like live theater but have since tired of the genre. Or did you mean something else?
Musicals are ultimately a hackneyed archaicism. Even the recently written ones. If your friend is tired of live theater, itself a hackneyed archaicism, you might be trying pretty hard to push a rope here by trying to interest them in the most hackneyed of the hackneyed.
I’m going to suggest, as many have done before that what matters is what sort of music or story the friend might like. I enjoyed Cats. I’ve also enjoyed many of the other older musicals cited above.
But overall, how much I enjoy a musical is how much I’m directly nostalgic for the specific tunes in it, the specific story it tells, or how novel and modern it is. That’s just me, but it points out that why somebody likes or dislikes anything is unique to them. The idea of a universally attractive entertainment is a mirage.
They lack enthusiasm for it. I was hoping maybe there was a show that would engage their interest.
I think I’d like the show, but I listen to the songs on Sirius XM’s Broadway Channel, and I can barely understand the lyrics. Same concern regarding Hamilton.
I don’t know the age or condition of the OP’s friend, but in general I can’t understand most of the lyrics and 25+% of the dialog in any stage production. Same with movies or TV.
It is very tedious to sit for 90 minutes watching a spectacle with little to no idea why people are doing what they’re doing.
PSA: Folks, if your ears still work well, protect the crap outta them. Because once they don’t work well, life gets lots suckier.
It might be a bit of schadenfreude on my part but I think of this whenever some person drives by with their car speaker volume turned to 11. A day will come when they regret that.
I loved the wordplay in Hamilton. My ears are beginning to go, and i dread losing that.
But back to the OP,
So, what styles have they already decided they don’t care for? Definitely pick something different.
Speaking as someone who lacks enthusiasm for musicals, taking me to a decent performance of “anything goes” or “guys and dolls” isn’t going to change my mind.
Don’t take him to a show that everyone who likes musicals likes, take him to something that shows him there are other kids of musicals out there that he might enjoy.