Lila Downs, one of Mexico’s most vibrant musical stars for a few decades now and a global ambassador of the nation’s culture, sits in a house in the capital Mexico City, about 250 miles northwest from her home in Oaxaca. She’s not there as an artist, but as a mother.

“My older young boy is 14 and we’re here getting his teeth fixed,” she says, idly weaving her hair into long, black braids as she talks on a video call. “I live in Oaxaca ...