The first and hardest mental obstacle would be cynicism. Humans have a remarkable capacity for it, and most people really would have to see the spaceship land with their own eyes before they accepted that it was an actual alien rather than a practical joke/ hallucination.
However, once you're past that, I think the human mind is pretty robust. You'd need a genuine
Outside Context Problem to break it, and they seem to be pretty rare events.
The thing is, a true OCP has to be beyond not only human experience but also human imagination, which has come up with all kinds of crazy crap over the years. It certainly seems to have explored every tiny possibility allowed for by known science, as well as a load of stuff that isn't.
For example, an advanced alien race invading Earth would not be an OCP. We've never encountered such an event, but even those who don't believe an alien invasion is ever possible are at least familiar with the concept, thanks largely to H G Wells in 1898.
In other words, even if some huge, slavering, unspeakable inter-dimensional cyber-hell-beast uglier that Geiger's worst nightmare was to materialise in Hyde Park tomorrow and start turning people inside-out with inverto beams issued from its uncountable nameless orifices, people would still have a mental category to put it in, because they've seen 'Alien' and they've seen 'Mars Attacks'. Sure, they've never seen anything exactly like this before and they wouldn't know what the thing was, or how its technology or biology worked, or how it had got here or why, but the details are irrelevant. Once their cynicism has been inverted along with Granny and the family dog they would be able to instantly recognise it as a "scary-*** alien monster bastard with some kind of advanced technology". With the phenomenon safely pigeonholed, they only have to survive long enough to get over the initial shock and then their minds will be ready to start reacting to the situation in character. For some people that will mean picking up a gun, for others negotiation, for others runnning away and hiding. I'll leave you to argue which would be the best course of action in that particular situation.
Of course, the real problem is that we have no way of knowing whether or not there really is anything out there beyond human imagination, and we never will, because there's no way of knowing how much you don't know. An OCP is, by definition, impossible to predict or even conceive of before it happens except in the very vaguest of terms.
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Ag! AG! Agag! AgAGAagaAG!