If your parents are concerned about sexual content, I believe there's a setting somewhere where you can disable you seeing nsfw. Every once in a while, it might slip, but it's not like you can't just ignore it and maybe unfollow. I'd also reccomend xkit, because there you can block posts including certain words/tags, block a specific post all together, and all sorts of other helpful stuff.
As for why you should have it, not only is it a source of humor but it's also a great creative outlet, and a place for you to make friends, share your drawings, and such. There's content about literally anything you can think of, so no matter what you like, you'll find others with common interests.
I guess I'm supposed to be helping, so I won't list all the bad, but I won't promise you won't get a little attached to it, among other things like gore and the aforementioned sexual content, but, like i said, there can be precautions put to prevent all that. Like Preach said, tumblr is very safe as long as you're mature with it.
Hope this helps!