In the demo, the Prussian capitalists treated the Industrialists as their primary Interest Group. The Junkers were made up of landowners representing the aristocracy, while the Intelligentsia represented people working in Academia. The list goes beyond these three, all of them being neatly listed in the game's Politics menu. While it's easy to paint everyone with a broad brush, pops can actually support more Interest Groups, as the individuals that make them up don't necessarily agree on everything.
Ideologies are an important aspect of Interest Groups in Victoria 3. Prussia's Industrialists happened to favor Individualism, having their own stances on welfare, education, and other topics, and generally favoring private over public funding. In some countries, however, Industrialists may not be Individualists.
Each Interest Group also has a leader whose personal opinion has a lot of weight. Going back to the Prussian Industrialists, they were led by a man who happened to be a Royalist, which would lead those Industrialists to oppose abolishing the monarchy. Since you're dealing with several Interest Groups, you can track the political strength of the pops supporting each one.
While you might be inclined to cater to their demands, you can also motivate them to rise up and overthrow the ruling class. This can be done by knowingly passing laws that they hate. Choosing this path obviously means that you'll have to fight them, but it's worth knowing that other countries may also get involved.