Questions & Answers about Это всё равно не повод спорить.
All three are close, and context decides the best English rendering. Всё равно literally suggests all the same and is used for:
- anyway / in any case: It’s still not a reason to argue.
- still (despite what was said): Even so, it’s not a reason to argue.
- it doesn’t matter (less literal here, but possible): Either way, it’s not a reason to argue.
Повод is more like a pretext / excuse / occasion (a “trigger” people might use to justify an action). Причина is a more neutral cause/reason.
So не повод спорить often implies: Even if it’s true, it’s not a good enough excuse to start arguing.