Agree with asumption of @FranHefner. From your screenshots, it seems that the local time on your device it too far away in the future or in the past with the IC. Usually this issue can be solved by synchronizing the local time.
Thanks @FranHefner and @peterparker indeed that was the issue, the clock was not using the automatic beacon from Apple, but just the Mac’s internal clock.
Everything works fine.
But this is intriguing, why is this enforced by the IC?
Every other website, including banking sites worked flawlessly, and so did the InternetComputer.org site, it was just these two critical websites that did not work, and probably DAPPs did not work, I just did not test yet.