What are you talking about, Craig? That is exactly how passwords work. If you change so much as one bit, you get logged out. On the other hand, with biological systems, both beneficial and neutral mutations very much do exist. You’ve got your comparison completely the wrong way round.
In any case, trying to draw a distinction between “biological information” and Shannon information is nothing more nor less than a rescuing device to try to salvage an argument that is objectively, factually and mathematically untrue. Mutations and natural selection very much can add new Shannon information (through insertions and duplication for starters) and this is perfectly consistent with the second law of thermodynamics because Shannon information and entropy are to all intents and purposes the same thing. It is also a rescuing device that doesn’t work because there is no clear definition of “biological information” let alone any way to quantify it and measure it. If you can’t quantify it and you can’t measure it, then you can’t even start to make any claims about whether or not you can add to it.