

A lightbulb (a plain old incandescent lamp) is typically brought up as an example of resistive load.

Yet the filament is actually made of several feet of very thin wire cleverly coiled to form a filament which is about one inch long. Clearly coiling the wire this way makes the filament more or less similar to an inductor. Yet lightbulbs are not considered inductive load.

Why are lightbulbs considered resistive load with a filament made of coiled wire?

The reactance at 50 or 60 Hz is simply negligible. According to this calculator a coil of 100 turns 1 mm diameter, 25 mm long is 0.04 µH. At 50 Hz that's 12 µΩ. A 60 W bulb at 230 V has a resistance of 880 Ω, then the 12 µΩ is only 0.014 ppm of that, and the cos(φ) = 0.999999999999999902. Shall we say "1"? 

The filament isn't coiled to add reactance, but to increase the resistance, by making the filament longer. Higher power bulbs don't need the higher resistance, and therefore often don't have a coiled filament. The alternative for increasing resistance would be to decrease the filament's diameter, but then it would become too fragile.
