Is it more true to say that Jupiter (and the other planets and asteroid belts and dust clouds in our solar system) orbits the Sun, and the Sun orbits the barycenter? The barycenter that the sun revolves around is influenced (marginally) by the other bodies in the solar system and not just Jupiter. If the definition of a barycenter is to be interpreted as this image suggests, that would mean that no material object orbits another material object and they instead orbit their collective center of mass somewhere in space.

no material object orbits another material object and they instead orbit their collective center of mass somewhere in space.

That’s exactly what happens. Why do you think this is incorrect?

It seems to fundamentally change what it means “to orbit” something.

As I understood the term, orbiting would be used correctly in these cases:

• A lighter object orbits a heavier object, and both of their paths of motion are elliptical about their barycenter

• Two objects of identical mass orbit each other, and their paths of motion are circular about their barycenter

In contrast, the image above implies the following:

• A lighter object does not orbit a heavier object; they both orbit their barycenter with an elliptical path of motion

• Two objects of identical mass do no orbit each other; they both orbit their barycenter with an circular path of motion

Even the Wikipedia page for barycenter, which OP linked to, opens with the following:

“the barycenter… is the center of massof two or more bodies that orbit one another and is the point about which the bodies orbit.”

Perhaps “orbit” as a verb has two meanings, depending on the specificity of the context.

No, your earlier definitions are incorrect. All orbits happen around the barycenter. The only question is whether one of the bodies is large/massive enough that the barycenter is located within it

I mean, the Wikipedia page for Jupiter says “Jupiter orbits the Sun”

Just because a more accurate description exists, doesn’t mean that the less accurate description is fundamentally wrong. Depending on context, the less accurate description may be perfectly suitable for the subject at hand. If your priority is to be the most correct, then by all means go ahead and use the more accurate description.

I think this logic applies to a lot of things.

I take issue with how the meme says “Jupiter doesn’t orbit the Sun”, which rejects one valid and common way of using the verb “to orbit”.