So, my question is, how is it possible for very intelligent people, including Linus Pauling, to still hold onto their assumption that crystals had to be periodic?
Linus Pauling advocated for a hypothesis called twinning in which grains of periodic lattice were joined together at an angle, such that you got non-standard symmetries on a large scale that did not exist at the atomic scale. His argument was that there were plausible alternative hypotheses that had not yet been ruled out by the evidence.
While Pauling probably pushed his certainty too far, there is a sense in which this is how science is supposed to work. Confidence in scientific conclusions is only justified when a determined attempt to refute it by competent and motivated opponents has been made and has failed. A hypothesis gains in confidence only as all the alternative hypotheses get rejected. Thus, for any hypothesis to be justifiably accepted, you need systematic sceptics to try to attack it and pull it apart. It's like evolution by natural selection - only the fittest hypotheses survive. So in this, Pauling was acting as a good scientist, trying to pick holes in the theory, and challenge it for as long as it could be challenged.
You should also consider the psychology of people like Pauling. There is a tendency in human social interaction to fit in with the crowd, and follow the intellectual fashion. That's fine for learning and applying what's already known, but is an impediment to discovery. Scientific revolutions are made by mavericks who can stand against the consensus, and who can stick to their own beliefs against all the slings and arrows that the community can throw at them. Pauling was likely as successful in science as he was because he had such a stubborn, contrarian, self-confident personality. Of course, while such a personality is very useful to persist and push your theory against dogmatic opposition when you happen to be right, it can be a drawback for the individual on the occasions that you are wrong. Although, as I said, science needs such people to continually challenge and test the consensus, it is a reminder that we are all fallible, even the cleverest of us. And personality is not the same thing as intelligence.
It's common for a field to take some time to get used to new ideas. Mathematicians took a long time to accept negative numbers and complex numbers. Physicists spent many years after the invention of General Relativity rejecting the possibility of black holes - even Einstein once wrote a paper proving them to be impossible! The German physicist Max Planck said that science advances one funeral at a time. Or more precisely:
A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it.
