不変性 is "immutability" and 不変的なもの is "immutable things", which refers to things that do not change over time. It's not a very common word, and as far as I know, it does not have a tricky meaning in the field of music. So you have to figure out its implication from the interview itself. They are basically talking about how 不変性 is not important to the interviewee any more. They are using this keyword in several ways in the interview.
- メディアの不変性: They are thinking physical CDs are more "immutable" than music delivered via the network, and he thinks CDs are not important (at least concerning this song).
- スタイルの不変性: His style/policy as an artist is not immutable. In other words, his style is changing.
- 歌詞の不変性: He has written lyrics that can be appreciated regardless of age or culture, but this time his lyrics contain words that may not make much sense in the future/past.
Actually, there is also a word 普遍性, which is more common and is more suitable in the context of the last bullet. I kind of feel they are using 不変性 and 普遍性 interchangeably because they cannot be distinguished in an oral interview. So when "immutable" makes little sense, try reading it as "universal" instead.