After several years of building its own software to connect mobile apps in its cars, Hyundai Motor Co. is throwing in the towel, becoming the first global auto maker to embrace software from potential rivals Apple Inc. and Alphabet Inc.’s Google.

It may not be the last, according to drivers and industry researchers. New car buyers are asking for vehicles that have Apple’s CarPlay and Alphabet’s Android Auto, which control the dashboard displays now providing drivers with information and entertainment—and perhaps future revenue...