The problem (for the bank) is they are now liable in the UK[1] if you are defrauded because someone installs malware on the phone. There's basically zero upside for the bank to allow customers to use F-Droid, since probably 0.0001% of their customers would do this, compared to a vastly greater number of customers being tricked into installing random malware on their phones.
Accessibility settings are a tricky one since that's a separate law. I wonder if they whitelist screen reader apps from the official app store. Anyway that's not the case in the original article.
From the bbc article, the number of fraud rose 12%, and you're presuming 0.0001% would be using F-Droid. Is preventing that an efficient ("reasonable") action from the bank ?
Accessibility settings are a tricky one since that's a separate law. I wonder if they whitelist screen reader apps from the official app store. Anyway that's not the case in the original article.
[1] https://www.bbc.co.uk/news/articles/cy94vz4zd7zo