Wow. Considering that star charts aren't your cup of tea I have to thank you on the double for taking the time to reply. Thanks!
Also thanks for your all your input. I will explain everything below and believe that your misinterpretation is due to the fact that the website itself is only available in German.
There is a difference in hostile and access to the system. Hostile/habitable only refers to the presence of habitable planets or moons in the system (or the absence of such) while the access colors green, orange and red tell you if you can freely enter the system (green), need a permit (orange) or are not allowed to enter the system or parts of it at all (red).
Since Earth had a cataclysmic event on December 27th 2.156 AD it is off-limits to all spacecraft since. Reason is that the volcanic eruption of Yellowstone blew some micro organism into the atmosphere that aggressively destroyed all NBO (nano bio-optical chip technology society did rely on) on the planet. By enforcing a strict blockade ever since Humanity managed to contain the microorganism on the planet itself. That's why it is off-limits.
MORRE Station is a hostile SYSTEM meaning there are no habitable planets or moons (but a space station). Access to the system requires a permit (orange). I hope this clarifies it a bit?
You are absolutely correct (see above). Hostile/habitable refers to the system's planets supporting Human life or not. The background colors indeed show political affiliation to a certain factor. So Barnards Star is Earth Alliance controlled space (blue) and the system itself is controlled exclusively by EA and supporting life (box with white background).
SOL has a pentagon instead of a square since it is home to the Mars Colonial Council which obviously is tied to Mars. All this is explained in the German blog posts on PANEC.de.
Again, thanks for your questions and input. I hope my answers help you understand my intentions better. Cheers, Oliver