Cookies
Firefox worked beautifully for me to access my banking payments until about 3 weeks ago. Now I am getting the same message from it that caused me to stop using Chrome and Safari. The message is that cookies are blocked. I believe I have enabled cookies in settings although it is not stated in those terms in settings.
Wšykne wótegrona (1)
Have you tried clearing the cookies and cache? Sometimes corrupted data can get in there and cause issues with a specific site. See this article for how to do that: https://support.mozilla.org/en-US/kb/clear-browsing-history-firefox-ios#w_clear-individual-site-data
We might also need to lower any Tracking Protection settings. This site might be sensitive to that. Try the steps in this article to do that for this specific site: https://support.mozilla.org/en-US/kb/enhanced-tracking-protection-firefox-ios#w_turn-tracking-protection-off-for-specific-websites-only
Also it might help to know which banking site you're having this problem with. We might be able to see if this site frequently causes login issues for others on different browsers since you mentioned it stopped working on both Chrome & Safari, which is highly strange.