How can you hope to play correct notes on the organ, if you don't know the meaning of accidentals?
This is precisely what happens to a lot of organists.
They hear something is not right in their playing but since they don't know what's the difference between C# and Db in the key of their piece, all they can do is grope.
So what's the difference, let say in F major, between C# and Db?
If you see Db on the score, and that's F major, you'll know that it's a harmonic major because it's a lowered 6th scale degree.
If you see C#, chances are it's no longer in F major because C# would be raised 5th scale degree and you don't suppose to raise or lower the constant chordal notes of the tonic chord (1st, 3rd, and 5th scale degrees). Maybe it's harmonic D minor (7th raised scale degree).
How can you know all this just by playing organ music?
That's what I'm talking about. Those theoretical differences are only apparent to people who have good working knowledge of music theory and harmony.
So these people when they hit the wrong note, they immediately recognize the key, the chord, and the meaning of that accidental. And they fix it right away.
There's more to sharps and flats than meets the eye.