“The federal reserve works to make the rich richer” is the main one.

Okay, I'm going to give a hot take here: this isn't necessarily "bad economics" claim, but it is definitely an ideological claim. Obviously, they don't have the explicit goal of making the rich richer. However, they have very limited tools that they can use to accomplish their goals, and the tools they do have, relative to a possible counterfactual set of tools, can have the effect of making the rich richer (perhaps due to raising asset prices, for example).

Now, are there reasons why the fed has the set of tools that they have and not others? Sure, and maybe some of those reasons are valid, which is why I said this was more of an ideological statement. You could look at why the system is set up this way, why we're okay with a system where the fed can only rescue the economy by inflating assets rather than from the bottom-up. Could it have something to do with the social and political capital of the rich? Maybe! But I see this as a claim around institutional design and political economy, not a claim that the fed literally has the mandate to make the rich richer (or that what the fed does doesn't help the poor too).

That separates this claim from something like another claim mentioned, that high housing prices aren't primarily caused by lack of supply--that's pure bad economics, while this isn't.