All "Weavemasters" (i.e. all of the Chosen of Mystra and Azuth) can use both, as they are absolute masters of the Weave, and can see how the Shadow Weave relies on it, and so work through the Shadow Weave. Analogy: if you built a skyscraper and are still up in the... #realmslore

But guessing Mystra or Azuth wouldn't be terribly happy about Elminster dipping his toes into the Shadow Weave? Or have they kind of accepted that the Shadow Weave is here to stay and a part of the Weave, for better or worse?

From my reading of Ed’s answer, I think you’d find Weave masters can work through the Shadow Weave to access the Weave (they use the anchor points that Shar created to allow the Shadow Weave to “drain” the Weave), thus they never truly use the Shadow Weave