You mention 'cost saving practicalities' several times in your comment, however you haven't mentioned any. I'd be interested to hear them.
They could be wrong (and they have been before, of course) - but this family isn't arguing that. They are arguing on religious and privacy grounds.
Reductio in absurdum: take the "I won't do it because it's the mark of the beast" to it's next level (hacker news comments, library membership, news articles, theaters), and you have a dysfunctional society.