If, outside of our control, your password and mine matched except for one character and that near match was public knowledge, would you object to me publishing my password here in cleartext?

There's a big difference between publishing your own thoughts - which may have nothing to do with what your family thinks - and publishing your DNA, which is inextricably tied to that of your family. It's my data, which I have a "natural" right to share as I see fit, but it's also very similar to yours, which you have a right to keep private. These rights are incompatible, one has to give.