I don’t think so. I have always for years had that option to disable cross-site traffic enabled, and never had a problem.
After I posted this vanity, I launched Chrome, set it up to allow cookies, but enabled cross-site traffic blocking (third party cookies) and it doesn’t work in Chrome either.
I disabled cross-site traffic blocking (allowing third parties to see where I have been browsing) and it works fine.
I am pretty sure it is that setting.
I think something is afoot.
They seem determined to see (or allow someone to see) where you've been going. Have you tried the 'browsing in private" feature?