you're arguing that I should undertake to understand somebody's beliefs about the positioning of all 214,000 miles of coastline in the world before I try to understand their intentions about where they're navigating to
I'm not arguing that and I think it's a pretty blatant strawman and that nearly any independent observer of this exchange would agree. This makes me pretty averse to continuing this conversation.
You seem to be proposing that in an argument about politics, I should engage in a depth-first search. Here's the issue: I can knock down all of their arguments, and change not a thing in their mind. No matter how many "How" arguments are defeated, there are an infinite more laying in wait. To change a mind, you must address the -Why-. You must direct your arguments to their motivations.
No. I think one should never ever engage in an argument about politics to try to change someone's mind unless your interlocutor is that very peculiar individual who will alter their beliefs based on new evidence. To the extent the above description is true it is evidence that people don't form political opinions based on evidence and that's a good time to stop arguing with someone about their opinions.
all I need to know is that they want to go to Jamaica because the weather is nice.
The weather is nice in Haiti too. Also, in High Communist Cuba and (parts of) apartheid South Africa. "Opposing universal health care" is like "opposing going to Haiti". "Sure it the weather sounds nice but you've overlooked dozens of other issues". It doesn't usually mean you're opposed to nice weather.
It wasn't my intention to strawman you. If my interpretations of your arguments are incorrect, I have absolutely no idea what you're trying to convey, except possibly a big "It's complicated!" - which I don't disagree with, and if that's supposed to be a counterargument, it's misdirected.
As for people discarding evidence, proving "Brand A of universal healthcare is Bad" doesn't say anything about brands B-Z - again, my point is that you seem to be suggesting I should focus on implementation (or is that a strawman?) details rather than...
As Multiheaded added, "Personal is Political" stuff like gender relations, etc also may belong here.