The most boring debates in metal usually involve genre purity. The best way to kill off that factionalism is to go right to the heart of the experimental stuff -- which means appreciating the rhythm anarchists in Meshuggah, the hyper-complex atonalists in Behold the Arctopus and the song-structure experimenters in Voivod.
Despite the differences in each band's sound, there's one thing they share, which is an awareness of their relatives over in the genre we call "classical" music. You can't have the splattering, exploding variation of instrumental attack in a song like "Disintegore" without the total-serialism of Pierre Boulez's second piano sonata (try the first movement "Extremement Rapide"). Likewise, Liturgy guitarist and songwriter Hunter Hunt-Hendrix cut his composing teeth on minimalists like John Adams (whose Chamber Symphony has a final movement that fuels its rhythm sprints with riffing electric bass work). You can hear that influence in a classic, minimalist-generative piece like "Generation."
The longer song structures of art-metal bands such as Krallice and Kayo Dot are informed by the New Complexity crew: names like Brian Ferneyhough ("Flurries") and James Dillon ("birl"). In these composers' works, the random-feeling attack patters of Boulez get turned up to a very metal "eleven." Even when it's not loud (and the music is often loud), the intensity will be unmistakable for fans of progressive metal.
This corridor of influence and fellow-feeling isn't one-way, either. Some classical composers, such as the Italian Fausto Romitelli, obviously sketch their arrangements with an awareness of post-metal textures and timbres, from Gorguts onward (see the "Finale" of Romitelli's An Index of Metals album for some thrashing woodwinds and brass -- and then check out his album Professor Bad Trip). For additional modern classical riffage, go immediately to "Machine V" by minimalist composer Marc Mellits.
The Bang on a Can street-marching band the Asphalt Orchestra has even arranged Meshuggah's "Electric Red" for its own stomping, summer-parading instrumentation. Along with one of the first heavy, experimental (and siren-using) orchestral works, Edgard Varese's "Amériques" and the grinding, snarling string quartet by Iannis Xenakis ("Tetras"), you can find all these pieces in the appended playlist. Don't you dare call it un-metal. And if you're a fan of modern classical, open up your ears to the gratifying complexity that metal has been offering for decades now.