@chesney I'm a parent of 3 daughters, the oldest about your age. I would definitely want to know. I would want to be able to support her through this, know any triggers, help with any legal things. And just to love on her a little extra.
Now... YOUR parents. First, I think what they've said to you about tinder dates is complete unacceptable. I have other words, but we'll stick with that one for now.
That said, these are your parents and they said what they said. They believe what they believe. You are dealing with enough right now and it is not your responsibility to educate them. Not now.
Your story is YOURS. You can tell it when and how you choose, in as much or as little detail as you choose. My advice is to tell them the central fact. They should know, IF you feel that they will support you and care for you. They do not, however, need to know the details (who, how, etc). That is yours and you can piece it out to them as you feel comfortable doing so. Or not at all- your call.
Right now you need support. Tell them what they need to know in order to provide that. As you get stronger and are coping better and they, possibly, grow a bit... you can choose to share more.