Note that the quoted article says absolutely nothing about "weather on Earth". It's talking about "dramatic changes in our solar system", i.e. a distortion in the shape of the termination shock, which lies 75 to 90 AU away from the sun. That is an effective boundary between the heliosphere and the ISM, where the solar wind and the interstellar wind are equally dominant.
Neptune orbits at 30 AU, but the "solar system" is understood to extend at least to the Oort cloud, 50000 AU distant. Earth orbits at 1 AU which is well inside the heliosphere, where the solar wind is much more important. That's why these spacecraft have to look at neutral helium atoms, which are the only interstellar wind components that can actually make it down here without being deflected by solar magnetic fields. Outside the solar system they have a rough density of about ten helium atoms per mL.
This has much less influence on the Earth's climate than the "sunspot activity" referred to by politicians, but you can expect to hear a lot of crap soon, e.g. "Weather on Earth might be shifting in part because of human activity, but larger context in which the Earth moves has some trends to deal with as well".