Not an example of Bayesian inference
Sympathise with the motive of this article but generally not impressed.
The example given has nothing to do with "Bayesian" logic. The author doesn't seem to understand the difference between Bayes theorem, a mathematical result which no one disputes, and Bayesian inference, which is a controversial stance in philosophy of science and stands in contrast to frequentist inference.
No frequentist would dispute the logic of the given example - there is nothing objectionable to a sane frequentist about using population frequencies and Bayes theorem in this way. Nor is there anything wrong with using your best guess of the population frequency if you don't have it exactly (though you can do much more nuanced stats than a single guess, there's no need for a short article to go into that).
The controversy is over the extent to which one can equate "belief" and "probability". It's a thorny topic and this comment is long enough already.
The author is right this is a religious war that will bite you if you jump into ML or stats, but yet another "explainer" from someone who doesn't really understand the subject isn't much help.