Perhaps I'm unreasonably fussy, but if I had a circuit needing gigohm isolation, I'd expect to have to clean the board rather thoroughly.
I can see how it can be a problem with high-impedance op amp inputs and high-impedance signal sources. Besides, its resistance is proportional to distance, so it'll be lower where clearances are tighter. I actually experienced problems created by a conductive flux, and even though in that case it was of the order of tens of megaohms, I now avoid fluxes that are even slightly conductive.
I clean all my boards anyway, but some hard to reach spots will always remain uncleaned, so cleaning does not solve the problem completely.
Finally, there are many fluxes that don't conduct at all (at least at low voltages), so there is no reason not to reject one that measures higher than 0.0 nanosiemens. But many of them have other disadvantages: some produce too much fumes, some are very hard to clean with IPA or wash off the hands after an occasional contact, etc. So I am still in search for my holy grail.