My wife's MacBook Air (2012), El Cap 10.11.6, Safari 11.12.
As of yesterday, suddenly cannot display nytimes.com or boston.com sites. When accessing either, their content displays for about one second, then goes either to a completely blank screen (NYT) or shows only bare navigation text (boston). I have disabled or uninstalled Ad and content blockers, no change. No other sites of many I've checked display this behavior. I suspect some change in the website authoring, as both are commonly owned. Of course, both Chrome and Firefox have no issues with these or any other sites.
If I can find a saved Sierra 10.12 or High Sierra installer; I may bump it up to see if that works. Don't want to do Mojave on that one as many apps she uses are still 32 bit so would likely no longer work under 10.14. If anyone has a similar config on older hardware/OS/Safari, check and see if this weirdness happens for you. Thanks.
My Mid 2012 MacBook Pro OSX 10.11.6 works fine on Boston.com surfed thru all topic choices at top of page.
Tried NYtimes.com page loads foe about 1 second then goes totally white. Refresh page and the same thing happens over and over. Then tried it using Firefox Quantum ver 63.0.3 (64 bit) and it worked great.
I have found on some sites, not necessarily the Particular ones you mentioned, when I see that issue I have to scroll down the page a ways to actually see the contents. I don’t remember which sites, specifically, but I think possibly Huffington Post, Wired or Salon.
So, this afternoon, the NYT page and Boston.com are again loading correctly, as mysteriously as they were failing last night. My wife does the NYT crosswords, and there were user comments reporting exactly the same failing behavior using a Mac laptop and Safari, but Firefox/Chrome not fazed.
Had to have been on the server/source side.
Donna, FYI, there was zero content, with no scroll bar to indicate hidden content at the bottom.