Why the Radio Shack LX5 and derivatives have inverted tweeter polarity

There's no obvious reason for it.  The crossover is first order, which normally doesn't need it.

I have a cynical explanation.

Actually, it's quite curious that the nominal crossover points for the reactive elements in the crossover are 3300 for the tweeter and 1300 for the woofer.  That works because the woofer has a lot of resonance above 1300 Hz.  Even with the choke that large (1.0 mH for the LX5 and it seems 0.9 mH for the LX55) there is still a tendency toward bulging at 3kHz or so.

I think Radio Shack tried to lower the cost as much as possible, and rather than using a slightly larger choke, say 1.2mH or so, to get flat response at 3kHz, they instead reversed the tweeter polarity, which  also flattens the 3kHz peak (it lowers in the range 3kHz-8kHz).  They were less concerned about the loss at higher frequencies.

So, it was an attempt to make the speaker cheaper than doing it the right way, with a larger choke.

Now, this is just a guess, it could alternatively be the Linneum tweeter requires that inversion for some reason related to its polar response, which is so hard to understand anything is possible.