Generally speaking, you should trust someone whose professional or experienced more than some random stranger. Especially if it's not one person but a large group of experienced professionals (most of the controversial "anti-science" issues today).
But it's actually important to "do your own research", and not just listen to authority. Provided you actually know how, i.e. you can find accurate sources and distinguish fact from fiction. Because even the most qualified, unbiased, genius authority are occasionally wrong. The big issue today is that a lot of people don't know how to research and distinguish lies, but (although it's probably impossible for most) finding a way to teach someone how to find the truth, will always be more effective having some authority tell them the truth.
Key example: doctors often miss symptoms and diagnoses that a patient can discover on their own. It's not that the doctor is stupid or unqualified, in fact they have way more medical knowledge than you. But the doctor only has a series of questions and maybe a few tests to make a diagnosis, whereas you have the full experience of symptoms and an internal understanding of your "normal". IMO people actually should "play Internet doctor" and research their symptoms, not to reach any 100% conclusions, but to suggest diagnoses and tests to their real doctor.