Clicking off some or all of the trackpad features may help some, but not me. I took my machine to an Apple store and could not believe they told me the problem is in the way I type! I told them for $1,400 the machine should work for me and not the other way around. From the other fixit comments it’s obvious the problem is not fixable at their end. They did exchange my Air for another one, but it does the same thing. Hate to say it, but I have modified my palm position to keep the cursor steady. I think we will see future laptop keyboards being touch screen; the new touch bar feature on the Pro is the tip of that spear. I also think Apple will eventually do away with these books entirely, and make the pads the only choice for portable computing.
I am having the same problem with my MacBook Air, just two weeks old. I tried unblocking all of the trackpad commands, but not only did that not work, the commands still operate! And this is after rebooting as well. I was able to find a jury-rigged solution, however. By taping a 3x5 index card over the trackpad, along the top edge of it (there will be some trackpad surface showing at bottom but my palms don’t reach that far) I seem to have mostly anesthetized the sensitivity, and as a bonus, can still use the trackpad features through the card. I still plan to bring the machine into Apple, since it is unacceptable to pay so much money for something with such a basic flaw; and it appears from reading these comments it has been going on for some time.