Well, in order to challenge my core beliefs, you should know what they are… 
The interesting part is not the one where he (potentially) ruffles feathers of American readers (Jefferson is a footnote in History abroad the USA, btw), but the part about the backfire effect, the amygdala and how challenging ideas are responded as physical threats… and very specially the conclusion in which we can learn to identifiy that primal response as what it is, and open our mind, listen, and change when is necessary.
I’ve been fortunate enough that, despite that I am a passionate person, one of my core beliefs is that knowledge is good, and the path to knowledge is truth, no matter how bitter, challenging or poignant it is. And this is why I am open to listen and change when my opinions and beliefs are challenged… but that doesn’t happens very often as my opinions and beliefs are built on a solid foundation of knowledge, and most of the time, the people challenging them is less knowledgeable on the matter than myself.
On the specific topic of global warming, I haven’t seen “An inconvenient truth”. When it was first released, I already knew more on global warming than the vulgarized version of reality shown on the film. One of my hobbies (even if is a masochistic one) is to fight and debunk denialism of reality… GW denialism, 9/11 conspiracy theories and Holocaust denialism are topics on which I’ve written more words than you’ve ever read about them -true. 
And guess what? I’ve never changed a single mind. Most people just aren’t lucky enough to learn the truth and go around blinded by a haze of lies, beliefs and fear of challenging ideas. And that’s fine, most of the time. It only gets on my nerves when they murder people over that bullsh¡t…
Addendum: the study linking vaccines and autism was bogus and was largely isnpired because the author had a commercial interest to sell vaccines with a diffferent chemical composition than the ones he pretended to prove that could cause autism. “Buy my vaccines, the others cause autism because I say so” is a terrible marketing strategy and ended up with him debunked and imprisoned for fraud… just the news never made it to antivaccines because it would challenge one of their beliefs and antivaccines, as many other fanatics, are not about the truth.