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This book from 1889, presenting a scholarly study of Christian hymns, has the following phrase:

It may be said, and with truth, that the Magnificat of Mary, the Nunc Dimittis of old Simeon, and, above all, that the Gloria in Excelsis Deo of the angels at Bethlehem, antedate this hymn of our Lord and His apostles. It may also be said, and with the same truth, that these furnished to the early Christians their earliest expressions of praise. But it appears that the Last Supper, with its pathetic union of Jewish and Christian ideas, was also the place at which the Psalms of David and the spiritual songs of primitive Christianity were united. The thought that this reveals is larger than these limits will permit us to discuss. It is in brief that as Jesus Christ came, “not to destroy, but to fulfil,” He designed to show to His Church that gratitude, love, trust, and adoration were to be combined in all future psalmody. The t’hillim of the Jew were to become the hymni of the Christian.

Now, according to the OED and Wiktionary, there seems to be further meanings of this word than that related to pity (perhaps the most used nowadays). I think the author does not intend to use the word in that sense. What is the intended meaning here?

PS: the paywalled/full version of the OED lists 6 meanings of pathetic.

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.