With regard to Reg's nuts-n-bolts suggestion, I've seen these antennas
far too often and in far too exact a 45 degree state for them to be
simply loose hardware.

The ones I've seen didn't look accidental either.

So - other suggestions? Any support for the 'storecasting' idea? One
place I saw one of these was on a MacDonalds, another was a bank, so
Muzak would make sense. Still, why would so many be off-polarized?

Muzak or similar services may do their own transmitters in some places, they
frequently operate on subcarriers on the local FM stations.

I've seen them on fast food places as well.

Plot by space aliens to kill us all with junk food?

Clueless installers covering both bases when they don't know the
'real' polarization? Some special service that transmits at that odd
angle?

Poissible, but it takes some effort to get to 45 degrees, most antenna booms
are pre-drilled for 0 or 90.