If I were you, I wouldn't mention the nsfw content to your parents because that could make them a little more suspicious of the site (though there is a safe-search button you can turn on when you're looking through the tags). I would start by telling them that there aren't any viruses on it (but if you get fan-mails of people asking you to go to their blog and click on a link on it, don't), there's a lot of good content on it, and that it's overall a good website.
Honestly, the only "bad stuff" I've seen on it is the occasional nsfw (like I said before, you can turn on the safe-search filter).
Slightly agreeing with Skulleh here.
Yes, there's a side of Tumblr that's toxic and disgusting and there is NSFW content, HOWEVER: That's not the entirety of Tumblr. As Skulleh said, you can only see posts from the blogs you follow so follow people who'll post something that you'll want to see.
EX: If you want to see posts about Tokyo Ghoul, then follow a blog that posts about that. If you want to see posts about dogs, then follow a blog that posts about that.
For another example. Me.
I like Black Butler, so I follow blogs that post about it and what they post are lovely fan-made images, fanfictions, headcannons, AU's, etc.
Then there are the problematic people that will send me hate because I support a certain ship, or because I don't ship something. What happens to them? I either make a witty or an intelligent reply and leave, don't respond to them, or I simply block them.