My personal experience with self harm and relationships -
I used to self harm a fair bit due to a past relationship (many silly teenage tears were wasted on this guy), thankfully there was no permanent scarring or marks left over.
My current partner (going on for four years with him in August) knows I've self harmed before, and it didn't stop him falling for me and dating me (obviously). However, he really dislikes it whenever I mention it as he has really strong opinions against it, thinking it's selfish and many other things - despite this, he is accepting of the fact that I've done it before and I obviously regret it. He just wants to make sure I don't do it again.
I don't judge him for his opinions on it because we are all entitled to our own beliefs, and I myself thought that about self harming as well (before I felt terrible enough to do it myself).
If someone isn't mature enough to date someone with self harm scars, then they aren't worth it - they represent a troubled past, and nothing more.