I agree MAC addresses can be personal data - if it can be linked in some way.
So a mobile phone? Sure - it links to you through subscriber info etc.
A router? Sure - links to you via your ISP (although im both cases technically it links to the person paying the bills)
But a DAB radio? Like others have said, unless you registered it under your name then its MAC is not linked to you.
We then go back to the tests of whether it actually is personal data, and one of those tests is whether a person can determine who you are by taking reasonable steps and also whether they are likely to try.
In both cases, in the real world the answer is arguably no.