Thankfully, I can fix most of these problems by enabled the built-in dark mode for the second website and getting a browser extension for dark mode on the first. It doesn't fix the drop down menus though.
I'd like to make a suggestion to disable dark mode on specific websites so I can still use it but also easily avoid these issues.

First image: https://www1.flightrising.com
It works mostly fine, except for the site status blurbs on the right side. They are rendered completely unreadable because the text is lightened but the background is unchanged. This issue is also present in other parts of the website.

Second image: https://finaloutpost.net
Again, the text is lightened but the background unchanged. I'm going to assume this is because they're using an image as background and images are unchanged?
On the left the same thing happens with this drop down menu.