I’m confused about the “purposes don’t affect the world” part. If I think my purpose is to eat an apple, then there will not be an apple in the world that would have otherwise still been there if my purpose wasn’t to eat the apple. My purpose has actual effects on the world, so my purpose actually exists.
So, yes, basically this is what Dennett reasons in favour of, and what Rosenberg is skeptical of. I think the thing here that needs reconciliation—and what Dennett is trying to do—is to explain why, in your apple story, it’s justified to use the term “purpose”, as opposed to only invoking arguments of natural selection, i.e. saying (roughly) that you (want to) eat apples because this is an evolutionarily adaptive behaviour and has therefore been selected for. According to this view, purposes are at most a higher-level description that might be convenient for communication but that can entirely be explained away in evolutionary terms. In terms of the epistemic virtues of explanations, you wouldn’t want to add conceptual entities without them improving the predictive power to your theory. I.e. adding the concept of purposes to your explanation if you could just as well explain the observation without that concept makes your explanation more complication without it buying you predictive power. All else equal, we prefer simple/parsimonious explanations over more complicated ones (c.f. Occam’s razor). So, while Rosenberg advocates for the “Darwinism is the only game in town”-view, Dennett is trying to make the case that, actually, purposes cannot be fully explained away by a simple evolutionary account, because the act of representing purposes (e.g. a parent telling their children to eat an apple every day because it’s good for them, a add campaign promoting the consumption scepticalof local fruit, …) does itself affect people’s action, and thereby purposes become causes.