Thank you for replying so quickly!
Regarding your first message, I actually found out because another person e-mailed me (US-based) saying they couldn’t access the website so presumably they were not accessing it twice (before and after I added and removed US from the list) and yet the site was still down for them. I also tried on another device of mine that wasn’t used for the original test, and it was also down for me.
Yes, I have restored the site to the point before I installed the plugins because of the site down issue. I do also have a staging site that I can use for testing. So, I have just tried to recreate the issue there. In other words, I followed the same steps, adding US to test and then removing US from the list. So, shortly it should be unaccessible if accessing from the US and not logged in to the site (oddly, even in the other circumstance, it would allow me to go to site/wp-admin and log in, and everything worked fine…it was only logged out users that would be getting the constant refresh issue).
Last time it took a while (maybe an hour or so, for the issue to start).
Here is the staging site: https://rxtranslations.staging.wpengine.com/