Safari blocking bank bill pay

I have two financial institutions where I cannot use their bill pay system because of something in the most recent Safari update- 13.0.4. Both sites give message that cookies have to be turned on for the site to function, as if they are blocked. But in fact they are not - "block all cookies" is unchecked in Safari Preferences. I've not seen anything where Apple acknowledges this problem or that it plans to fix it.

Firefox works to access bill pay at both institutions. Thoughts, workarounds?

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