Yes and no, in my opinion. The reasons why music must be good are different from the reasons why lyrics must be good. It’s a bit like comparing apples with oranges, I think. In one sense, the answer must be yes, because we’re talking about the gospel, the word of God. That is the thing that makes lyrics especially important, and means we must get them right. One of the risks of not getting them right is that we will misrepresent God, which we mustn’t do (E.g. we could slip into heresy or idolatry, or just plain old shallow, ill-informed theology). The other thing that we can do wrong with lyrics of course (often not mentioned much in my circles, since we tend to focus more on “correctness”) is just make them unpoetic, or unengaging. All the best songs in the world have gripping lyrics. So yes, lyrics are critical. They carry the message, explicitly.

But I would argue that the musical side in a sense is just as important, but its importance is measured in different ways. The tune carries the message, perhaps implicitly, or indirectly (as distinct from explicitly or directly as in lyrics)

If a song has a brilliant tune and harmony, then regardless of how good or bad the lyrics are, people will quite likely want to sing it! If it doesn’t, they won’t. You then do the lyrics either a service or a dis-service, but how important therefore is the tune, if it can make people either sing or not sing the lyrics!

Think of what happens when the melody is good and the lyrics are poor… people sing bad (or shallow) theology. And you can’t stop people getting into it because they love the music. The music has a power over people that ‘correct theology’ doesn’t have. I’m not denying the power of the Spirit to work through poor tunes! I’m just saying they’re operating in different realms, pulling on different heart strings.

In summary, I don’t think it’s a good idea to put lyrics and tunes up against each other, since both need to be good for a song to be considered good. Perhaps it’s better to focus on the consequences of doing each poorly. The consequences of doing lyrics poorly are far greater than the consequences of doing tunes poorly. With one, you can commit heresy or idolatry. With the other, people simply won’t sing the songs.