Yes, people often choose ignorance. But most of the time, most people do so rationally. Does each of us know who won each college football game this past weekend, and which players contributed what to the results? We could ... but odds are, many of us "don't feel like it," and are therefore ignorant about who's up or down in the BCS standings.
If you want to talk about the educated populace, scientists often choose to stick with what they know or believe, as documented in Thomas Kuhn's "Theory of Scientific Revolutions," which noted that sometimes new scientific theories could not come into prominence until the highly-entrenched supporters of the old theories had died out. For scientists looking at competing theories in their field, this should be inexcusable. But educating oneself can be highly time-consuming and costly.
For the average Joe, keeping up on all the options, facts and alternatives for all the possible opinions they could hold would easily be several full-time jobs, and that presumes they have the scientific training to read between the lines on the write-ups of medical studies and identify whether the experiments had hidden biases or poor controls that might skew the results. Or they can just keep their "ignorant" beliefs about things which don't matter too much to them on a daily basis and focus their education and attention on the things that matter to them. If fingers are pointed anywhere, Elon Musk is right: they should point at the journalists who are paid to research and write about these things so that they can inform us accurately.
Given a limited amount of time in my day, I'm not going to be researching car accident rates, adjusting for the age/reliability of the technologies chosen, the skill of the driver, the road conditions, the vehicle age/reliability, etc. I already have to research and decide where to invest my savings, research and decide the best route home after a long day at the office, and choose which of 70 cereals (let alone other breakfast products) to pick up at the store.