Can an app with root permission access another app data? I have an rooted android phone and use root apps like greenify regularly.

Recently i have installed my Bank application on my phone and the bank application is not allowing me to login as my phone is rooted. Even in last pass also it gives an warning that it is vulnerable as my phone is rooted.

I wanted to know whether one app with root permission can access other apps data. 

For Example: 

I have given complete root permission to greenify and can greenify access the stored files on some other application just like lastpass(I haven't given root permission to lastpass. I knew lastpass encrypts data on client side too. But i wanted whether it can access the data irrelevant of its encryption ) .
Yes -  if you grant it root privileges, it can Theoretically access any other apps data ( granting / denying is by "Superuser or Su" which is used to manage applications which are allowed to gain root access). That is a con of rooting. But if the data is encrypted it shouldn't be able to unless it is a rogue app which is capable of doing so

Aside, if you want to bypass bank app restrictions, you can try measures suggested here Get around an app that won&#39;t work on rooted device. Also see other Root Hider apps thanks to Izzy for pointing that out 

Detection of root is done on the app as explained here Root detection by server or app ( do read the comment of acejavelin in case you are planning to hide root)

Also see How do I protect my phone from malicious apps once it is rooted?