Magic Johnson's 20-year-old son hit the Sunset Strip, hand in hand with his boyfriend ... and his parents couldn't be happier for their kid.

Earvin Johnson III -- aka EJ -- is one of Magic's 3 kids. The Lakers legend tells TMZ, "Cookie and I love EJ and support him in every way." Magic goes on, "We're very proud of him."

The feeling is mutual ... 'cause EJ told us he's been "hoping and praying" for his dad's team, the Los Angeles Dodgers, ever since Magic and his business partners took over the franchise.

He's also a huge Lakers fan ... obviously.

EJ -- who's a student at NYU -- has a close relationship with his parents. Back in August, Magic tweeted, "Thx to my son EJ for hosting me at NYU. Look forward to taking him to dinner tonight in the city."