Through what context did western music, at least since the advent of notated music, consign almost all percussive instruments to strictly military music until quite recently? I assume percussive instruments/drums had some specific connotations in western culture but what lent them these meanings and how did they maintain their particular place without penetrating non-military European music, religious and otherwise, for so many centuries?
The key factor, regardless of however else you parse it, is industrialization. It's not that drums were never used in other situations before - it's that it was hard to get the opportunity to. Simultaneously with the greater usage of drums, orchestras got bigger, novel brass instruments appeared, and the pianoforte saw major changes. Bulky instruments could be transported by rail now. Everything was getting louder, with more refined timbres and better playability, because of technology improvements. All of this radically changed the scope of music, producing wave after wave of musical innovations - and it hasn't stopped, even today.
The tabor sound in this video is much less "snappy" than a modern snare. It's useful for march, since it's relatively portable, but in an orchestral setting it doesn't offer as many possibilities as, for example, a timpani. And in popular music, the instrument needs to be both small and allow flexibility of performance, which rules out bulky drums, but does allow some smaller hand percussion instruments like shakers. The drum kits used in jazz and rock, for example, became plausible to carry to a gig only after the automobile reached mass adoption.