How do unpitched percussion instruments not have a pitch and how does whatever noise they produce not potentially create dissonance with the music they complement?

They do have a pitch, however because it is percussive as opposed to sustained, we don’t register the pitch as easily. Many will also purposely obfuscate the pitch, such as cymbals, they don’t hold a tone, but rather multiple tones at once, making a washing sound and working for any key. If you ever look at a cymbal you will see the rings and divots around the cymbal, because if they weren’t there it would ring like a bell which definitely has a pitch.

As for the drums themselves they definitely do a have a pitch and it is common for to tune them in fifths, or octaves. Think of a drumline, those drums all have pitches and tones, they also function identically to a traditional drum kit. You can very similarly to the cymbals obfuscate this tone by doing an offset tuning so your drum head resonates unevenly across the head creating multiple tonalities at once.

You can achieve this by being lazy and not tuning.

I’m a professional sound engineer and ex-professional drummer BTW.