The polymer works by destabilizing the cell membrane. A mutation which reduces the efficacy of that mechanism would, in fact, promote resistance to the method. Whether or not the polymer design could be modified to adapt to that change (and what the costs of this might be) are an open (and very interesting) question.
However: it's virtually certain that widespread and indiscriminate use would promote resistance to the existing design and method.
This is true, except the polymers in question work not on a cell activity principle but on a chemical disassembly potential [1].
This would be analagous to humans evolving to the point where you could not kill one by shooting it in the head with a bullet. It could happen, people with their central nervous system in some part of the body other than the brain would survive a bullet to the head, and there are bullet to the head survivors, for whom brain structure may play a role, but it isn't a huge risk associated with shooting people in the head.
[1] "They try to mimic what the immune system does: the polymer attaches to the bacteria's membrane and then facilitates destabilization of the membrane. It falls apart, everything falls out and there's little opportunity for it to develop resistance to these polymers."
the polymers in question work not on a cell activity principle
That's not a necessary condition of evolutionary adaptation. Though I'll freely admit to being outside my bounds of expertise here.
Others have mentioned the lack of bacteria which have adapted to bleach (I haven't confirmed this myself through literature). My general sense is that there's a potential space in which possible solutions exist, and some solution are on the edges of that space, making them harder to reach and/or harder for multiple adaptations to simultaneously exist. There are extremophiles which survive in what would generally be considered extremely hostile environments (ice, high elevations, undersea steam vents, highly acidic geothermal pools, abiotic environments, etc.). Few of these thrive in more generally hospitable environments, presumably because the adaptations which allow them to survive the extreme environments also pose a comparative disadvantage to life forms which don't need to carry the evolutionary baggage / armor / support systems required to survive such environments.
Carl Zimmer wrote a few months ago about a simulation of evolution in which there wasn't a penalty for complexity, his musing on that aspect of the simulation are interesting:
In this experiment there was no cost to extra complexity–something that may not be true in the real world. The human brain makes huge demands of energy–twenty times more the same weight of muscle would. There’s lots of evidence that efficiency has a strong influence on the anatomy of our brains. Perhaps we might have more complex brains if we did. And if the animats had to pay a cost for extra complexity, they would evolve only the bare minimum. That’s an experiment I’d like to see.
> humans evolving to the point where you could not kill one by shooting it in the head with a bullet.
If there were billions of bullets flying around, and humans reproduced by the billions in a matter of hours with a generation-to-generation gap of minutes, this would happen in short order.
