Thanks. I long ago tried all the above suggestions. None of these gets at the problem.
My original post description of the problem included a truncated sample of the type of email hyperlink that fails to open, but I guess links not allowed in this message board, so it was removed.
Instead, I'll try to describe more exactly what is not working.
Like everyone these days, I have subscribed to several services which are based on a website with numerous articles/pages, but which send auto-generated emails with article summaries and embedded hyperlinks.
These links typically have the original domain-name URL prefixed with something like "email-st." and appended with "/click/" followed by a several hundred character long string of random-like characters, which are undoubtedly hashed data that the website uses to track which subscriber clicks on which link.
These subscription email links from most websites work reliably on my Mac, but one or two consistently do not. In cases where these links do not work, I always get the Safari error "Safari cannot connect to the server", followed by the full link, including prefix and long tag. This is regardless of what network I am on, home or elsewhere, and regardless of what DNS provider is being used. Also, when this error occurs I can always manually remove the "email-st." prefix and the long tag, and reach the main index page of the site, then find my way to the intended page.
Note that the 1-2 services that consistently give me this problem are not obscure, sloppily coded websites, they are large major websites, using, presumably, well-established third-party email subscription service providers. In terminal, if I run a "dig" or "host" command with the problematic email link URL, I can see that it is a proxy for redirect to the 3rd party tracking service provider's server.
Clearly, the problem is that Safari is somehow blocking the redirected link, but I can't figure out why. I have tried every permutation of every Safari setting and every browser extension.
Grateful if anyone can offer a clue on where to look to find the cause/solution to this.