I've been in that situation countless times, I can tell you people want to believe the scientific method works but there's always a reason they don't. Here's a few reasons I've encountered:
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Eroding trust in institutions: they don't trust the organisations or the people doing the studies. IMO news cycles play a big role in this; a study with a catchy result "A glass of wine a day is actually good for you" - by itself already a misrepresentation of the results - gets all the headlines. The countless of studies that prove no amount is good for you doesn't get any.
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They believe science is a book of solid answers, while it's merely a methodology to find better answers. People have a hard time accepting this.
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Post-information age: every bit of human knowledge at our fingertips is a true monkey's paw. A real overload of information has people exhausted, they rather listen to someone like them than have big words thrown at them by scientists.
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Misrepresentation of data: I cannot stress enough how easy it is to misrepresent data. Without proper context any piece of data can be framed to fit a narrative. Studying statistics was so counter intuitive, you'll never be able to convince people going on instinct.
Honing in on where people get stuck can help you get through to them. I know this will sound corny, but if you talk to people from person to person, not being judgemental, and really try to listen, there's always room for change.