I'll stick to the question rather than re-visit the referendum campaign and "Project Fear".
Without arguing over the ethics of it, effective compulsory voting is a complete non-starter. Australia is often cited as an example (although there are numerous others to choose from. Under their legislation voters who have not been granted a postal or proxy vote must "...attend a polling place, have their name marked off the certified list, receive a ballot paper and take it to an individual voting booth, mark it, fold the ballot paper and place it in the ballot box"
Because the ballot is secret, nobody knows what the voter does to "mark" his paper.
The practicalities of enforcing people to vote (presumably coupled with the threat of fines) are immense. The authorities in the UK cannot even get everybody to properly register their names on the electoral role. The turnout at the referendum was the largest for a national vote in many a year. But even then some 15 million of those eligible to do so did not vote. How would it be possible to issue penalties (and see them paid) to 15 million people?
So to the "competency to vote". Many people participate in activities for which they are not strictly competent. The finest example of this is government ministers who move from department to department with no particular competency to operate in any of them (witness recently Dominic Raab. the then Minister for Exiting the EU, who had no idea of the amount of trade passing through the Port of Dover). Another example is juries. Ordinary members of the public are placed in a position where their judgement on what may be complex criminal cases can consign the defendant to lengthy spells of imprisonment. Nobody suggests that because they are not Queens Counsel they cannot do their job. In both those cases the people who do know the issues involved (Civil Servants and advisors in the case of Ministers, prosecution and defence advocates along with the judge) are expected to explain the issues in language they can understand. Nobody is competent in all issues relating to a referendum of an election. Some may, by coincidence, have some competency but most have none. If it is being suggested that only those competent to vote should be allowed to do so compulsory voting may be a little easier to introduce as the electoral register would probably be in the low hundreds rather than 46 million.