One would think that everyone involved in the parody series “Schmigadoon!” was in love with the sometimes hokey, sometimes magical musical genre. Not quite.The director Barry Sonnenfeld has never been a theater guy.“I am not a fan of Broadway musicals,” he grumped affably over the phone. “I’m not a fan of filmed musicals. I don’t understand why people would stop talking and start singing.”So Sonnenfeld, who is best known for the “Men in Black” movies, was a curious choice to direct the new Apple TV+ comedy “Schmigadoon!,” a series whose very title screams musical theater spoof.The showrunner, Cinco Paul, a fan of Sonnenfeld’s work on the highly stylized and intermittently musical cult series “Pushing Daisies,” was unaware of the director’s aversion until they were shooting last fall, mid-pandemic, in Vancouver, British Columbia, with a blockbuster cast filled with Broadway stars.“Here we are on the set,” Paul recalled, “and he’s half jokingly saying, ‘Why are there so many songs?’”If you count reprises, they number nearly two dozen — composed by Paul, who created the show with Ken Daurio — spread over six half-hour episodes that air starting July 16.An affectionate, knowing sendup of classic American musicals, “Schmigadoon!” stars Cecily Strong of “Saturday Night Live” and Keegan-Michael Key, lately of Netflix’s “The Prom,” as a contemporary couple in a stagnating relationship. On a backpacking trip, they stumble into a frozen-in-time, trapped-in-a-musical town called Schmigadoon, which they can’t escape until they find true love.Paul, who grew up on his mother’s Broadway cast recordings and played piano for musicals as an undergraduate at Yale, said he came up with the kernel of “Schmigadoon!” almost 25 years ago. Not knowing what to do with the idea, he put it away until Andrew Singer at Lorne Michaels’s production company, Broadway Video, mentioned their interest in musicals a few years ago. A match was made.According to Strong, Michaels is — like her — “a musical dork.” And the show brought on stage-savvy writers, including Julie Klausner (“Difficult People”) and Strong’s fellow “S.N.L.” star Bowen Yang.In Schmigadoon, the locals include the sweet, melancholy Mayor Aloysius Menlove, played by the Tony Award winner Alan Cumming; the moral scourge, Mildred Layton, played by the Tony winner Kristin Chenoweth; and the handsome carny Danny Bailey, played by Aaron Tveit, who got news of his Tony nomination for “Moulin Rouge!” during the series shoot. Other boldface names from Broadway include Jane Krakowski, Ann Harada and Ariana DeBose.Recently, Paul, Sonnenfeld and members of the cast spoke separately by phone about “Schmigadoon!” and their affinity, or lack thereof, for musicals. These are edited excerpts from those interviews.“Musicals are charming, and they’re so entertaining, but they’re also sometimes dumb, and sometimes they’re problematic,” said the series co-creator Cinco Paul.Adam Amengual for The New York TimesCINCO PAUL I wanted real musical theater people. I wanted people who did eight shows a week and had those chops, because I wanted everybody to do their own singing, and I wanted to capture that singing live on set to the extent it was possible. The amount of talent we were able to get was phenomenal and was unfortunately because they weren’t able to work anywhere — because theaters were shut down. In many cases, the parts were written for these actors.BARRY SONNENFELD When I interviewed for the job, I said: “Look, here’s the thing. I want to shoot this entirely onstage and I want to shoot it in Vancouver because Vancouver has really great stages and really good crews, and it’s also cheaper.” What was surreal and wonderful was that Vancouver was the only film center that was open when we shot. L.A. was shut down. New York was shut down.CECILY STRONG We had to go shoot our “S.N.L.” intros right before I left for Vancouver. It’s like, you’re around New York and you’re seeing all these theaters shuttered. It’s a little devastating. More