Juat looked at that article.
Essentially it's saying that you should [1] download the trusted bank app and not a spoof app pretending to be the bank, [2] don't click any malicious links that are sent from a hacker disguised as a bank, [3] avoid anything that installs a keylogger on your device, [4] visiting clone accounts that aren't the bank's URL, and [5] hackers intercepting your SMS multi-factor authentication.
This is just "protecting any of your digital data 101," not anything unique about providing routing information. Mind you, you do you; if you're uncomfortable, don't do it!
How do you prevent any of those 5? With 100% certainty? You don't. But 99% of the time, don't download anything that's not trusted, use antivirus software, type in the bank URL every single time, change your password semi-frequently, and use multi-factor authentication.
If you do that, there's lower hanging fruit for hackers to go after that are more worth their time.