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So based on my limited understanding, some luxury cars have taken to using their sound system to make the cabin quieter when on the highway or something (Active noise control via wikipedia). And I learned about destructive wave interference in high school physics.

First of all, this is a thing, right? Secondly, I know vaguely how suppressors work and they're not strictly "silencers", but would using some sort of sound system with "anti-noise" be possible for reducing weapon report? And if it's not feasible with technology or whatever IRL, without worrying about such limitations, would it make sense in an advanced society?

Noise cancellation is a tricky thing.

Noise cancelling uses a soundwave with an opposite "wave" to cancel the other out. But since its a wave you essentially create an expanding bubble from the center of the Noise. Since you cant have your speaker perfecrly on top of the center of the Noise you'll create an interference pattern: at some places the Noise is cancelled, at some the Noise is doubled!!

Noise cancelling works by using a sound you already know is going to be made and a range of speakers placed inside the room. For a project we could only cancel out repetitive noises that could be predicted. We also needed to know the way sound bounced through the room (far beyond my expertise) and where people would be to make sure the double-noise area's happened somewhere people wouldnt be. So if your Noise cancelling worked it would need to know the placement of every person upon firing your weapon and the environment you are in at the same time. Worse: with speakers on the muzzle you might stop the muzzle sound but not the sound of the bullet breaking the sound barrier.

I dont think Noise cancellation will work very well to silence weapons.

If the gun is suppressed and has subsonic muzzle velocity, then noise cancellation should work for the remaining noise. In practice I am not sure if it would be worth it as a suppressed gun firing subsonic ammunition is usually good enough especially if you use a captive piston ammunition. But you'd only need it at few locations so the cost might be low enough for the reduction in noise to be worth it.

The reason gun needs to be suppressed and subsonic first is because otherwise the gun will emit noise that noise cancellation is not really feasible against. You cannot really do anything about the shock waves caused by supersonic projectiles or propellants for example without raising questions why you are using a bullet at all instead of just weaponizing your technology to kill people without physical bullets. Same with negating noise from the propellant in general. If your electric system can negate it practically, you might as well skip the propellant and use your technology to directly drive the bullet without using chemical propellant at all.

So my answer would be that using it as a replacement for current "silencing" technologies would not make sense but it might be used in addition to them for minor gains.

The noise canceling waveform would have to have a similar amplitude to the gunshot. Gunshots are in the range of 120 up to 175 decibels. A speaker that produces such a loud sound will need a lot of power, as much as a kilowatt (maybe less if it is just a single shot, maybe more if its a big gun). A typical guitar half stack can use around 500 watts of power, but it is large - 4 x 12 inch speakers. This puts power and size constraints on your noise canceling system.

Physics is against you on this one.

Muzzle blast (which is the precursor event) is caused by the expulsion of a fairly large amount of high-pressure gas at very high speed. Any cancelling impulse will require the production of a similar event, but with negative pressure, in effect producing a transient vacuum. Furthermore, the amplitude of the vacuum is fixed (at zero pressure, obviously) while the muzzle blast has no obvious upper limit.

Finding out the peak overpressure of a rifle or pistol muzzle blast does not seem to be easily done on the internet, but here is an amateur attempt which suggests a peak muzzle pressure on the order of 5700 psi, or about 387 atmospheres. This would seem to indicate that you'll need a vacuum volume equivalent to 387 times the size of the gas bubble emerging from the muzzle. This will also require addressing the pressure wave produced by ignition of unburned propellant after it is expelled from the barrel (muzzle flash).

In effect, you'd need rather a large array of speakers very close to the muzzle which would operate to produce a local vacuum which would be filled by the muzzle gases, and I'm not at all certain how to this, or even if it's possible. The rate of pressure decrease produced by the speakers would very high (high frequency response) at the same time that the volume displaced would also be very large, and the two requirements are entirely antagonistic in normal speaker design. Subwoofers move a lot of air, but not at high frequencies.

If you're willing to set up your speakers as a shell at some large distance from the weapon, the idea seems technically feasible, but such a speaker array would draw a whole lot of attention to the presence of the shooter, which seems unlikely to be desireable. Plus, of course, it would not exactly be very portable.