With that out of the way, the best book I read regarding conflict and resolution has been "Conscious Business" by Fred Kofman. While his strategies relate largely to the business world, they are applicable in a very general sense. I bring this up because these strategies will help you in framing and explaining why this matters to you.
The main takeaway from the book is that you need to approach these problems from a place of infinite empathy. Remember, your final goal is not to "win the conversation" or have the last word, it's to come to an agreement of shared values and collectively (that means, you and your parents) build a strategy in combating the underlying problem.
To build that strategy, I recommend taking a page out of the Less Wrong sequences, and _Hold Off On Proposing Solutions_ [1]. Somewhat ironic given what I am currently doing, so I suppose I have already failed. Anyways, on this note, recall I said that the goal was an "agreement of shared values." Start here. Begin by listing your values and frame these in the context of the conversation.
As for the exact solution, it may very well be a matter of how you form beliefs vs. how your parents form beliefs. Being able to describe your epistemology and how it differs from their own is a valuable tool. However, it can often be difficult to carry a heavy conversation for long enough to get to the root of this. I point back at Fred Kofman, and having a well of infinite empathy. You have to be willing to commit a lot of time.
And to that last point (committing a lot of time), there are some stories out there of people being converted both to and from dis/misinformation. I've been thinking about this quite a bit over the last couple years. Fortunately, there are people who are better at this than I am. Jane Lytvynenko [2] is a wonderful disinformation reporter, and she puts out a lot of resources for how to spot fake news, how to look at evidence critically, how to critically examine online content, etc. She doesn't quite get to using Bayes' theorem, but dismissing fake news and contrived stories doesn't often rise to the level of needing Bayesian reasoning (although it does help!).
With that said, I'm sorry that you're encountering this with your parents. While few have commented, I think more than a fair share of people are running into this issue more and more. The most important part is the empathy, and remembering your goal. After that, the best you can hope for is enough time and energy to help drive the point.
[1] https://www.lesswrong.com/posts/uHYYA32CKgKT3FagE/hold-off-o... [2] https://twitter.com/JaneLytv