They (the investment/owner class) make their money work for them by investing and by playing the banks. Generally, they want to invest the vast majority of their money, and never cash out of their portfolio. When they need "cash" to buy something, they do it with loans and there's lots of tricks (that I'm not super familiar with) to make loans as cheap as possible, and potentially even profitable if their investments are doing better than the cost of the loan.

Now, why would they spend money pushing propaganda when instead they could be investing that money? Well, when you are that rich, you don't actually have to spend that much to push propaganda. People are already clamoring for your opinion, because they see you as successful and think, if I copy you then I too can be successful. And when you do need to buy an article, it's pocket change compared to your vast wealth. And if instead you need to buy a TV news network, a newspaper, or a website, that itself can be an investment. As long as you don't run it into the ground, it may make you money at the same time as allowing you to push propaganda.

And why do they want to push propaganda in the first place? Because if the working class (those that live off paychecks instead of investments) has the time, energy, and knowledge to do something about wealth inequality, then the investment class will start to have to pay their fair share and lose a bit of their wealth. The investment class doesn't want that to happen so they need to rob the working class of those 3 things. Manufacturing a culture war is one way to steal time and energy from the working class, because they now have to spend that time and energy on defending personal rights. Busting unions is another way to rob time and energy, as the fewer rights workers have, and the less they are paid, the more time and energy they have to spend to stay out of poverty.

It's all a ploy to get people to pay less attention to how the investment class gets their money so that they can keep racking up the score without interference.

That said, some of the investment class actually truly holds hateful views, as does some of the working class, but the working class has nothing to gain by acting on that hatred except a sense of personal fulfillment. The investment class benefits financially, so they may act out the hatred even if they don't feel it.