It's still just cherry picking 2 variables to graph together that may or may not be related.

Correlation != Causation.

If you care to read the article you'd find links to a more detailed study that demonstrates the exact portion of income inequality that is known to have been caused by de-unionization.

That's not how this works. There's no study here showing how they were able to discount all other variables and show a provable link between A and B.

This is data cherry-picked to support a conclusion and published by a lobby group (a pro-union one and publihed on labor day, no less. It's flashy!). You may agree with said conclusion, but this is research presenting a theory not a proof.

There is no causation being shown here. It's a possible theory, but that is all that it is.