What is the meaning of "pathetic" in this phrase?

I think that a more basic (and obsolete) meaning of 'pathetic' is to do with feelings. For example, the 'pathetic fallacy' is the belief that animals have the same feelings as us. So I'd suggest that 'its pathetic union of Jewish and Christian ideas' is referring to a similarity of feelings evoked by "the Psalms of David and the spiritual songs of primitive Christianity". Maybe a contrast with a more concept-based similarity is intended.

In this context, “pathetic” is best understood as the adjective form of “pathos” - as @PhilipWood says, essentially it means “having to do with feelings”.

The actual picture is considerably more complicated, because our modern taxonomy of emotion simply does not translate into the way people thought in the past. “Pathos” used to specifically mean “suffering”, and it still usually has connotations of sadness, longing, regret and so on. But also, when people in the past referred to “pathos” or “suffering”, they meant something more like what we would now call “feelings” in general, and specifically what one might call “narrative feelings” – emotions involving memories, intentions and hopes – as opposed to emotions like fear and joy which are purely organic reactions. (It is in those terms that “pathetic fallacy” makes sense. Of course a dog can feel excitement, and a storm can “rage”; the fallacy would be in thinking that a sunset mourns someone’s death or that crows herald bad news).

In the quoted text, I would take the word “pathetic” to refer to the meaning of feelings in hymns. The emotion conveyed by art is not “your” emotion - it is not caused by things that happened to you - rather, it is part of a design for how to think and feel about some external topic, and “pathos” refers to the emotional aspect of that design.