I never had a Walkman, or any other portable music player, for that matter.  But I have always had good car stereos, even back when what the factory provided really sucks.  I installed really good AM/FM cassette decks in my cars, starting with Concorde brand units. Those were incredible - response as good as the best three-head hifi or studio-recording cassette decks of the day.  Car-audio was my only form of portable stereo.  Still is.

So for me, not much has changed.  I listen to a lot of vinyl.  I record it on cassettes for my classic cars that still have decks.  Put MP3 versions of music on flash drive "pucks" for my more modern cars.

One thing that changed for me is back in the 1980s, I used to record some albums on reel-to-reel.  That way I didn't have to wear out albums for background listening.  My turntable and cartridge were very good, but still, I played my favorite music on reel-to-reel back then for background listening.

Now I do that same thing with DVDs.  I always buy music on vinyl and DVD, and I use the DVD media for background music and the vinyl media when I want to really enjoy.