It depends on what you mean by "Gore-Tex" since there are some variations of fabric/laminate structure depending on the intended use, i.e. "Gore-Tex is not a single product. However, the essential component of "Gore-Tex" is an expanded ptfe (Teflon) matrix partly or completely impregnated with a monolithic film of polyurethane. In spite of what the publicity may say, the water transport properties of Gore-Tex have absolutely nothing to do with the ptfe and are entirely governed by the polyurethane. The ptfe is there primarily as a reinforcing agent (and historical reasons). The water transport properties of the polyurethane depend on its chemistry and there is a trade-off between water permeability and strength. The expanded ptfe matrix allows Gore-Tex to use a more water-permeable form of polyurethane than that used by Sympatex, for example.
Water passes through the polyurethane by effectively dissolving in it. It is then a simple diffusion process that drives it from the high water partial pressure inside the garment to the lower water partial pressure outside. In fact, as the polyurethane increases its water content it becomes better at diffusing water so there is an element of "intelligence" that causes the Gore-Tex to work harder the wetter it gets.
So the pore size doesn't actually have much to do with the transmission of water vapour, it is the polyurethane chemistry. As already mentioned, nylon will also absorb water but it is nothing like as permeable as polyurethane.
I'm not sure about passing bromine through Gore-Tex, my instinct it that it will tend to react with the polyurethane turning it yellow.
I was told this by an employee of W.L.Gore & Associates Inc