Ernest was not just unpopular, he was widely regarded as a murderer. There was an attempt to exclude him from the throne in OTL even after Victoria was sworn in, and Whigs such as Macaulay mused about a second glorious revolution being necessary if he ever took power. And he was not just a person with a conservative mindset, but an extreme ultra-reactionary and he was literally the leader of the Orange Order for a while (in fact, the Orange Order got temporarily banned because Parliament believed he was plotting to use them in a military coup - that is the degree to which he was despised). You cannot really bring up Hanover in this scenario, as it had a vastly different domestic situation and a much, much stronger monarchy. Also, George I was so unpopular the Jacobites nearly overthrew him. There would almost certainly be a big crisis if Ernest ever came to power, and the monarch was not powerless in this era; there was a lot of trouble he could do with his powers of influence.
On your other point, "England's last experiment with republicanism" was also something which many left-of-center Victorians admired, they toasted to the cause of the Roundheads regularly against monarchical dictatorship, and they regarded Cromwell as a hero who fought for the religious liberty of nonconformist protestants - there's a reason he has a statue outside Britain's Parliament building. I hate Cromwell as a quasi-monarchical imperialist despot, but the Victorians did not view him that way at all. The French Revolution was also something which the Whigs generally admired, and the great hero 19th century Whigs admired was Charles James Fox who, famously, opposed Britain's war with the French Republic and Napoleon. Furthermore, there is the example of the United States as a republic, which is something which saw broad admiration as a model and an example of a free country among Brits (slavery, they chose to ignore).
I do suspect the most likely result of Ernest becoming King is a tussle of power with Parliament which he loses badly due to his immense lack of support and unpopularity. Parliament would be really intent on ending this crisis quickly and making this a second glorious revolution installing a different Hanoverian (the Duke of Sussex, maybe) to the throne, especially to avoid radicals out-of-doors from using this opportunity to their own ends. But there is a non-zero possibility of a more radical revolution, depending on how things play out.