Don’t power chords, used frequently in rock and pop songs, break the voice leading rule of no parallel fifths? As long as one of the other instruments (second guitar, bass) is playing the thirds of the chords, is this permissible?
Power chords have nothing to do with voice leading. Their purpose is to create a frequency mix that creates a reasonably identifiable sound in the presence of intermodular distortion. A single clean electrical guitar signal is rather sinoidal, adding distortion to it creates harmonics but no intermodular distortion. Even adding octaves does not result in harmonics out of the normal overtone spectrum. Adding the fifth above, however, results in distortion adding harmonics from the octave below the lowest actually played note.
A power chord is part of sound creation (like various ranks of a pipe organ are with registers like 8' and 5⅔') rather than voice leading, in the case of electric guitar playing usually followed by distortion.
If you start with more complex harmonic material before distortion, the result after distortion tends to be quite muddy with so many different intermodular distortions that nothing clearly is discernible anymore.
While power chords could be fed into other distortion devices (imagine two wind instruments feeding into a single kazoo, for example, or create a mandoline with a tambourine as its body, wait, that's a banjo) for similar effect, in practice they are mostly used in connection with electric guitars and either overdriven amplifiers or similarly sounding distortion pedals.
A power chord is only one voice.
Sure, technically there are two notes playing, but they blend together into sounding like one, which is why it's called a power chord: it feels like one really strong note.
If your goal is to have multiple distinct voices from the same instrument, you shouldn't use power chords (and probably also not distortion). If you want one super-strong distorted cool sounding voice, then power chords will do the job.
Think about some songs that use power chords. Do they really feel like chords? Imagine the Smoke on the Water riff, do you feel the harmony? Can you imagine the two voices moving independently from one another? Or does it feel like there's only one note that's just really strong? Most people would say the latter, I think.
In music anything is permissible. True, centuries ago, there was a 'rule' about consecutive fifths. At the time, it was sacrosanct. Years later, a lot of these 'rules' are broken. Look at blues, jazz, for two examples. Theory isn't rules, it's an account of what works well. Breaking the rules has lead to other kinds of music - not a bad thing in terms of development. The tritone was once rewarded by anything leading to death (!) but nowadays, it's an accepted sound.
(Partly in response to a question that got directed here), parallel fifths are of some importance in rock, jazz, country, Latin, etc. in the pop field. To explain, first, one must ask why parallels (fifths, octaves, etc.) can cause (musical) trouble. It's not that these sound bad (or good) though.
The problem occurs when one wished to have two or more independent voices. Parallel fifths and octaves (and unisons and octave-equivalent transposes of these) tend to sound like a voice dropped out. In most popular style music, the only really independent voices are the bass and the melody. If parallel fifths or the like occur between the bass and melody, it sounds like one of these is missing. So as an arranger, (or when jamming where everyone is an arranger in real time), one tries to avoid consecutive (or hidden) perfect intervals between the bass and melody. (This also applies in most classical music where the intervals against the bass are more import than than intervals between inner voices.)
As an experiment, one can take a popular song and (using Finale or some other scoring program) copy the melody into the bass line leaving the other parts alone. Then try with a more standard bass line (or walking bass line or both).
Essentially, centuries ago, people liked their music a certain way. To get their music to sound like that, they set some guidelines to achieve the sound they liked, one of which was "no parallel fifths". But people's tastes evolved. Flash forward to rock, and people start to like that "parallel fifths" sound. So they "invent" the idea of power chords, which they use for their preferred effect.
What can we take from this?
1) Different musical ideas get recontextualised over time, and fall in and out of favor between genres.
2) Genre-specific compositional guidelines (often mislabelled "rules") exist for a reason. They help to create an effect, and when determining whether to use one of the guidelines, ask oneself whether one wants the effect that it would create.