Why an issue with only three websites

iMac (Retina 5K, 27-inch, Late 2014), OS X 11.0.1, Safari Version 14.0.1 For the last year or so I've had trouble with a a couple websites. AT&T, Princess Cruises, and more recently attending a Zoom meeting. Switch to Firefox on the first two mentioned, no issue. For example, on Princess, when searching for cruises, I get to the point where I have selected a cruise, but then the Princess site says "Pricing not available for this cruise". I switch browser, repeat the process, pricing comes up no problem. Doesn't seem that I should need to change Safari settings for just 2 or 3 websites out of the hundreds I visit. As for Zoom, tried to attend a Zoom meeting last week, could not join. Switched browser, no problem. (A Zoom message came up suggesting I use Google Chrome!). I just chatted with Apple Support on this, they had me check settings, all were good, so they had me clear cookies/history. I doubt this will help but will see in the coming days. May move to Google Chrome permanently. Any suggestions appreciated.