This happened all the time in sf stories in the 1940s: the protagonist would see something strange happen, and his (generally his rather than her) first thought would be that he must be going insane. As I noted a few years ago, in some such stories the protagonist's belief in his own insanity even causes him to be unwilling to propose to his girlfriend.
As I think I've noted elsewhere (but can't find it), I don't have a lot of patience for the "I must be going crazy!" trope in stories these days. In 1940s sf, it would often go on for pages; the protagonist would really seriously be concerned about it, and would explore the question in some detail. But pretty much every such exploration is the same, so it starts to feel like a boilerplate section inserted for form's sake into every story in which something strange happens in the modern world. (Much like the boilerplate paragraph explaining the Many Worlds Hypothesis that was required by law to appear in every alternate-history story published before 1990.)
These days, the insanity question in sf is usually no more than a paragraph or two of lip service. But it does still come up fairly regularly. And it makes me wonder about how people really would react to Something Strange Going On in the real world.
So, a thought experiment: Imagine that you're you, living in the real world, and something happens (to you, or right in front of you) that's not possible according to your worldview. Say a plant starts to talk to you, for example, or a person who you're talking with disappears into thin air, or something that seems to be a gateway into another place appears, or a mysterious stranger comes up to you and demonstrates an ability to read your mind, or you encounter a Mysterious Magic Shop that wasn't there yesterday. Or you find a strange glowing orb on the sidewalk that appears to be made of a substance previously unknown to humanity. Or you wake up and find yourself in what appears to be a different time period or what appears to be another world. But don't pick at these examples too much; feel free to substitute anything that's similarly outside of most people's idea of how the world works. Note that I'm talking about encountering, firsthand, something obvious and clear and direct; not just a vague possibility or a rumor.
Now: What's your initial reaction? Are you interested? Curious? Scared? Upset? Do you assume that it's a practical joke? Do you assume you must be going crazy? Do you assume you're hallucinating? A drug flashback, perhaps, or maybe you decide it's time to stop drinking? Do you assume it's magic, or aliens, or the work of a human scientist in a secret lab, or time travel, or psychic abilities, or . . . ? Do you try to investigate (assuming whatever happened doesn't appear to be actively harmful), or do you run screaming, or do you stare blankly at the strange phenomenon and make "buh, buh, buh" noises?
I'm honestly curious about what y'all think your reactions would be. There's no Right Answer, and this isn't a trick question. I'm most interested in whether you would question your own sanity (and if so, to what degree/for how long), but I'm also interested in the more general question of how you'd react.