You can sort percussion instruments into two broad groups - "pitched" percussion and "unpitched" percussion. Pitched percussion can be out of tune just like a guitar... but pitched percussion doesn't include drums - it's the stuff like marimbas and xylophones.
The unpitched stuff, like drum sets, castanets, cymbals, etc. aren't pitched because of the way they work. And that exposes the flaw in the very beginning of your thought process:
a drum makes sound because it vibrates, it therefore has a frequency/pitch
All sound comes from vibration - a guitar string, the lips of a trumpet player, the column of air inside a flute, the movement of a sax reed, and so on. But only regular
vibration has a frequency. Irregular vibration doesn't, and it's called "noise". (And I'm not kidding - that's the technical term in acoustics.)
There are a lot of reasons drums produce noise rather than pitches, but they'll basically boil down to signal reinforcement. This is what causes something in the room to vibrate when you play a certain note (it might even be the drums that start vibrating!). When that happens, you've found a resonant frequency. Non-resonant frequencies don't last - they're dampened by the object itself.
Hit a guitar string, and it rings. The frequency is resonant for the instrument. Hit a drum head and it doesn't. You get your initial boom or bang, and that's it.
The few drums that are considered pitched percussion - tympani were mentioned earlier - can be pitched by design. You'll notice several differences between a tympano and a drum from a drum set:
1. The tuners on a drum set connect the rim to the shell, or to the rim on the opposite side. When these are tightened, it affects the tension on only a part of the drum head - you have to do each one individually, and you can't really get them even. The tuners on a tympano are connected to a mechanism that is smaller in diameter - when you press down on a foot pedal, the tuners all pull down and in
at the same time, allowing a fairly precise pitch adjustment. Modern tympani have the mechanism as part of the frame; older ones hid the mechanism within the bowl.
2. There's the bowl itself. Parallel heads, like those on drum sets, create a resonant chamber... the air bounces back and forth inside it, reinforcing some frequencies and dampening others. Without getting too technical about it, the more different lengths you have in a chamber, the more frequencies might be resonant. Think about how many different lengths you have in an acoustic guitar: the body depth, the upper bout, the lower bout, the length of the body, and all the angles you can get with straight lines inside that space. Compare that range to what you get with a drum, which has diameter and depth. A tympano's bowl is there to maximize the range of the straight lines you can get in the chamber.
Anyway, for those and other reasons, drums don't behave like pitched instruments. While they can sound "bad", they won't sound "off by a quarter tone".