Full disclosure: I have a PhD in chemical engineering and currently work for a company that makes plastic.
The study appears to do a good job of preventing background contamination per the experimental methods.
The study explicitly states that it's purpose is to demonstrate that the specific analytical methods they are using ~can~ detect these compounds in the blood. There is a big difference between developing an analytical method to detect a compound and determining that plastics are a ubiquitous contaminant in human blood.
The compounds were detected at very low levels, and they had reproducibility and lower limit of detection issues. They were pushing the detection limits of the equipment and methods.
The conclusion specifically states that the amounts detected may not come from what I would consider to be "ordinary exposure". If you read section 3.3, the authors state that the plastics that were measured could have come from drug delivery nanoparticles, polymer implants, and even tattoo ink.
I also think it's important to point out that the plastic contamination was found in its "whole" state. Plastics are pretty much inert substances. That's why they are so useful in food and human body implant applications. The fact that these compounds aren't degrading into something more dangerous is a feature worth noting.
I'm not saying they belong in human blood, but it's not like they are breaking down into carcinogens or anything. And as others have pointed out, we inhale all sorts of substances, many of which are known to be more dangerous than microscopic plastic particles.