How do I enable third party cookies on MACbook Pro running Safari 13.0.4

That ended up being the trick for me too -- even though it had always been disabled, apparently after updating to 13.0.4, the box had to be checked and then unchecked again before the sites could be accessed.

Do you see a Prevent Cross-Site Tracking option that you can turn off as a test?

Try enabling "Prevent Cross Site Tracking," quit Safari and reopen it. It worked for me.

I'm having the same problem. The main website our business uses is a frame within another website, and normally I tell our customers to uncheck "Prevent cross-site tracking" and then it works. But just like cesibly, today after updating to 13.0.4, I can't get into the site, even though both "Prevent cross-site tracking" and "Block all cookies" are both unchecked.