True.
And for union with Belgium to work, you need no religious divide.
And for that, you'd need to go back all the way to the Dutch Revolt (or make Frederick Henry an even better general), and there's where it gets tricky. William the Silent was himself a very religiously tolerant person (almost the stereotypical
politique), but many of the people in his coalition (especially the urban middles class) were extreme Calvinists, and William had to tolerate them or lose out on their support.
It was only in the early 1580's that the idea of making William the Silent the actual undisputed ruler of the country (which wasn't a Republic yet, just states unified under the Union of Utrecht) was brought up mostly out of desperation, and William was assassinated before that could happen. The States of Holland were literally about the make him Count. It almost happened to his descendants as well a few times (William III had to practically refuse the Dukedom of Gelre in 1672), so having the House of Orange be in power directly could be a way out for a somewhat more centralised, militaristic/expansionist* Netherlands.
*Not to say that William the Silent wanted to conquer the world, it's just that as a 'Burgundian' noble raised at the Brussels court, he believed very strongly in a unitary Netherlands, including the South and if possible even the Walloon regions. Of course, this being the 16th century, there couldn't have been more than a hundred people, all high nobles or administrators, who shared that goal.