You're completely misunderstanding the purpose of the make me move feature that Zillow has. Make me move is for those who aren't officially listing their house, but would gladly move/sell if offered the "right price." It isn't for those actively selling their home, and it also has nothing to do with being flexible on price. Make me move is specifically for those who are NOT actively selling their home.
You can chose to not negotiate on your price, but that is something totally different and occurs at a stage separate from listing and showing the home. Also, the list price is only one piece of the various negotiations that take place during a home sale. Honestly, you have no choice in the matter about how "serious" buyers are and your attitude is likely to drive off potential buyers - especially those who are educated in how home sales actually work.