Is the speaker impedance constant or variable?

Impedance will vary by frequency response.
Each model of any speaker will have a different impedance curve. This is based on the different drivers in the speaker (maybe crossover too??).

Speaker impedance IS reactive, and varies according to frequency. The original WATT speakers were notoriously difficult to drive due to a HUGE impedance dip in the lower registers ... not as much a problem when used with a sub and active Xover, avoiding those frequencies. For excellent discussions of this and other technical issues find "The Audio Amateur" and "Amateur Speaker Builder" periodicals online. There are also plenty of speaker design books that will explain the technicalities in a fashion I can't.

It will vary fom speaker to speaker and over the frequency range. Magnapans are pretty much a constant impedance though. Most speaker specs list a "nom" and "min" impedance. I belive that the "min" value is at the low end of the speakers responce. These values do come into play when selecting an amp to handle the speaker load.

...so the amps that have different output onto different loads will kind-of straighten out the speaker's curve?

A speaker has a voice coil. Coils are inductive in nature. The impedance of an inductor can be calculated by the formula impedance=2pifL or 2 times pi times frequency times the inductance. If you notice from the equation: changing the frequency will give you a different impedance for the same inductor. Therefore, your speaker will have different impedances for different frequencies.