When I first started paying attention to music, about 12 or 13, I listened to the crap that was popular at the time: MC Hammer, C&C Music Factory, ad nauseum.
The "grunge" phenomenon helped derail me from that pablum with Nirvana and Pearl Jam. Different, but still fairly mainstream.
Then my older brother brought home the double bill of Ministry's "Psalm 69" and Skinny Puppy's "Too Dark Park." At first I was simply befuddled. Noise presented as music, what a novel idea! Once I got past my initial surprise and could actually listen to the music, I was amazed at how good it was.
Around the same time Nine Inch Nails became popular. I love Nine Inch Nails, but is essentially industrial pop. I don't mean that as a slight, I'm a fan of pop music (even if I don't much care for today's "popular" music).
Couple things I learned about myself. The first I already knew; I'm a fan of the non-sequitur. A lot of the music I really enjoyed would start with a really strong song structure and then throw in an entire musical track that would attack what had previously been played. (Forgive my lack of musical language.) The second, I really, really enjoy hearing sounds that a lot of people would consider abrasive. Oddly enough, I find sounds equivalent to nails being scratched across a chalk board very soothing.
So give me some music that includes abrasive noise ever eating itself with its own complexity and seeming disregard for song structure (while slyly reaffirming its own structure), and I'm a happy man.
I don't really care about music being "industrial," but I enjoy music that contains the aforementioned attributes. One of my favorite musicians working today is J.G. Thirlwell, who has been heading a band called Foetus for several decades now. His music isn't so much industrial as it defies categorization.
That being said, I love bands like the carnival barkers Mr. Bungle and Wolf Eyes, which is a band that is literally pure noise.