Lot of websites won't work with Safari

Go step by step and test.

1. Force Quit Safari, launch Safari holding the Shift key down.

    How to force an app to quit on your Mac - Apple Support

    https://support.apple.com/en-us/HT203987

2. Startup in Safe Mode. 

   Start up your Mac in safe mode - Apple Support.  

    Quote:

    It also does a basic check of your startup disk, similar to using First Aid in Disk Utility. 

    And it deletes some system caches, including font caches and 

    the kernel cache, which are automatically created again as needed.

3. Clear History

    Clear your browsing history in Safari on Mac - Apple Support

    Please read the article before clearing history, 

    this is like a low level resetting of Safari without affecting passwords and bookmarks.

4. If Safari doesn't open a webpage or isn’t working as expected

    If Safari on Mac doesn't open a webpage or isn’t working as expected - Apple Support

I think I can explain what might be happening. If you are unable to access certain web sites and possibly getting a message that your browser must be updated, this is not an unusual situation. The reason is that web site providers and software engineers write their software to work based on standardized specifications. For some reason, recent editions of Safari have been erratically problematic. One thing that may work is to upgrade Safari or you can use another browser that does work as you have been doing. It is important to know that Safari is installed as part of the operating system and it normally it cannot be individually updated. Safari is typically updated when the computer's operating system (OS) is updated or upgraded. Finally, even if you are able to update Safari, there is no guarantee that it will be compatible with every web site. This is why many of us have more than one browser installed. To date there has not been found one solution to this recurring problem.