All of the old hymns that have been around a while, before we got all these man-made religions with messed-up theology.
Actually, there are a number of older texts that have theological error or contain shallow theology.
Fortunately, most of them have been dropped from the common repertoire because of this, but some still exist, more the shallow kind than the erroneous kind.
"In the Garden" is the first one I can think of. People get all up in arms because they think that song is "pretty" or something, but it affirms almost nothing distinctive about Christianity.
Most of the ones that would qualify are from the gospel hymn vein.
On the other hand, hymns with good theology:
There Is a Fountain
The God of Abraham Praise
And Can It Be
Holy, Holy, Holy
Love Divine, All Loves Excelling
Holy God, We Praise Thy Name
A Mighty Fortress Is Our God
Sing Praise to God, Who Reigns Above
O Worship the King
Praise, My Soul, the King of Heaven
and there are many more