With Twitter, I find you can click the log in button, and then there is an X to dismiss the modal with, which then lets you read the page. (And this is absolutely annoying, terrible UX, and I wish to God people would stop putting things on Twitter.)
The existence of these backdoors is a bad excuse these teams use to justify user-hostile UX. I had no idea this was possible, so for me this might as well have not existed. I simply skipped reading twitter threads when I was on a device I wasn't logged in on.
Sometimes I click a twitter link on a devices I don't want to login to (work machine). I ended up creating a second account for this exact reason, so annoying.