I don't believe it's incompatible with membership in a legal domain, but NATO has been relying on nuclear weapons since the dawn of NATO, and so NATO has tried to express solidarity over nuclear weapons over the decades. This has been an obstacle to some countries that were really trying to get rid of nuclear weapons and taking more what I call “progressive” positions on nuclear disarmament. There are some strong-arm tactics by the U.S. government to try to make sure that the commitment to nuclear weapons isn't watered down. It's in NATO's strategic concept, renewed in 2012.
When the Liberal government under Prime Minister Chrétien, with Lloyd Axworthy, tried to challenge it in Washington in 1999, they didn't get much traction among NATO members. At the same time, I myself feel that a principled approach would be to say that we should be open to embracing the nuclear prohibition treaty and finding our own voice for such an important matter as nuclear disarmament.