Hey Zephyr, As a parent myself I dont stop my kids from listening to what they want, I enjoy the music of today myself, but sometimes if theres a bit to much swearing in the lyrics I may say to my 13 yr old delete that from your mp3 as he walks around the house singing away and not holding back...
I've heard slipknot and I'm not fussed on them their really heavy and hard to understand, so mabe your parents just hear the loud thrashing of that pacticular style of music and make their judgement from that. You should introduce them to something a little calmer to start with, and build a trust up with them, if they think they have reformed you, you could then go back to the music you enjoy...
May I also suggest get some headphones so they cant hear what your playing....
Good luck mate and they really do have your best interest at heart, even if it doesn't seem it......