I have never had the lack of a college degree hinder me in my radio career. With that said, my career spans 35 years. Times change. In addition, I never sought positions in public radio where a degree carries much more weight.
I was playing vinyl, slinging carts, backtiming to network news, and splicing tape when I started. Every station had a 3rd class with broadcast endorsement on the clock every hour they were on the air and usually a resident first class licensed engineer on staff or one a phone call away. In small towns where a drive to a major city was a day-long adventure, if you had a 3rd class and wanted to work at their station you were pretty much hired on the spot (at minimum wage more than likely but you could live on minimum wage then).
I am fortunate to be beyond the point of a degree determining my qualifications but there were points in my career when if I had wanted to take the Public Radio route I might have had the lack of a degree hurt me.
Being in the Houston area, I will say schools like Alvin Community College pump out students that know what they are doing in logistics and seem to have a grasp of what radio is while realizing they are 'new' in their cycle of learning just what day-to-day life is like inside the radio station. I think they even allow one to take classes on specific subjects. And, I might add they have a great station I wish had full market coverage. The folks coming out of the school don't just have book knowledge.
A big complaint from some degreed and broadcast student graduates is an attitude that the station's way of doing things needs to be changed to what their instructors taught them, but I never found that attitude from Alvin Community College graduates. It's natural for them to think they learned the best ways in school because so many instructors are radio professionals with great track records but they don't realize ownership dictates so much. It's as I would imagine acting. You might think the storyline might need some tweaks but you were hired to play a part, not rewrite the script, so you play your part to the best of your ability, period. With that said, I think a good radio person is always thinking how to make every segment of the station operation better...it's how you learn and grow, but you keep those opinions to yourself.
You do not need a degree to get into radio and make it but a degree can help depending on what you choose to do in the business. I'd say on a scale of 1 to 10, a degree is a 2 or 3 on the scale in regard to working radio as a career. It is true your passion, ability and attitude are much more important. If you are serious about your job, exhibit an ability to handle the position, are always honing your skills and learning as well as playing well with others, you'll get the nod in almost every case. If you're applying at an University owned NPR, that degree comes in pretty handy.