By these criteria printing press was much more programmable than the loom. The Babbage's machine was not notable for being "symbolically programmable", it was a machine capable of universal computation. That is huge step beyond any complex programmable automata such as were made for clocks and music boxes.

The "It had no conditional logic or flow control. No stored symbolic instructions." you mention applies to the loom too. It copied what was poked into cards to different medium, not unlike Gutenberg's press did.

I'm obviously missing the big differentiator of Jacquard's loom, but so far I have not seen it clearly explained in the articles I've read.