In this case the word “so" means “therefore” because the word “it” doesn’t refer to space, it refers to a statement in a previous sentence of the article:
Gravitational waves are ripples in the fabric of space, created by
movements of massive objects.
Both of your examples are grammatically correct. However, neither sentence conveys the meaning of the original sentence you quoted because the source is describing the statement “Gravitational waves are ripples in the fabric of space” as counterintuitive; it’s not describing space itself as counterintuitive. If the word “it” did refer to “space” then the meaning of “so” would indeed be “because" here.
"Normally we don’t think of space as having properties at all, so the idea that gravitational waves are ripples in the fabric of space is counterintuitive."
The confusion here seems to be a result of the fact that personal quotes in news articles are often taken from a conversation with the journalist, so the exact context isn't always clear. But in this case it seems fairly straightforward; he's stating that ripples in the fabric of space seem counterintuitive because we don't think of space as having properties (as opposed to something like ripples in water, which we do think of as having properties).