Going to be hard to use the same language as politifact when it's unclear what people mean when they say "boy" and "girl", but here is how I would parse Cruz's statement if I were going to make an effort to interpret him to mean what he intends to mean:

federal government is going after school districts, trying to force them to let (children with XY gonosomes) shower with little (children with XX gonosomes)

and politifact's response:

(children with XY gonosomes who believe themselves to be female) aren't (children with XY gonosomes who believe themselves to be male)

I think the context makes it clear they are deliberately misinterpreting Cruz because they don't like his vocabulary. That's dishonest.

Trump's quote says "real unemployment". I think you could fairly criticize the statement for invoking the no true Scotsman fallacy and for failing to adequately explain his terms, but it's clear he is intentionally rejecting the standard unemployment calculation. It should come as no surprise that then that the values don't agree. That doesn't make the statement a lie; that makes it uninformative. It's like if I told you "only five good movies came out last year" and you responded "that's a lie; 55 movies were certified fresh by Rotten Tomatoes." Your statement is more informative than mine, but clearly I'm using different criteria from you and that's not the same thing as lying.

In any case I think the point of the graphic is not " the ones on the left are actually true" but rather "these are all comparable, but look how biased the judgments are". That's a fair critique.

As you said they could be cherry picked. Hell they could all themselves be fabrications. The only one I checked was the Trump one.