Hello
As a fan-fiction reader myself, I think I can help you out (though I certainly am no Scholar of Canon Law, I have thought of this myself).
Basically, you should treat fan-fiction the same way you would treat any other art form. It’s not morally wrong to look at, say, the Venus de Milo in the Louvre even though she’s naked.
The moral question comes when you view graphic fanfics for the purpose of pornography. It’s happened to me loads of times when I’ll be reading a great story from my favorite fandom and suddenly BAM there’s a gratuitous sex scene. Not that I’m much of one for sex scenes, but as long as I don’t view it for pornographic purposes and see it only as art, it’s all good.
It also depends on your comfort zone. Some people can read very explicit material without getting phased, whereas for some even a little bit is too much of a temptation. It simply depends on how your brain functions.
As for advising you on what to tell your parents… that’s not up to any of us on the forums. They don’t seem at all concerned about fan fiction in general, so don’t worry too much about it, but if you have questions, you should ask them.
To sum it all up, if you at all feel bad or wary of temptation, etc., skip it. If you can view it simply as art/an enjoyable walk in the fandom, go for it. I know how hard it is in a lot of fandoms to find good fics that aren’t just plain smut. But so long as you just keep a bit of a wary eye out, you should be fine.