There are two incorrect questions here.
First of all, Windows XP is not necessarily less safe than an unknown new operating system, especially if it’s a new windows version. It’s probably equally unsafe.
Second, why would someone need to change their online banking password if they don’t have one?
It is true that a newer operating system can still contain security vulnerabilities but Windows XP is particularly vulnerable because it is no longer actively supported by Microsoft (i.e. there are no official patches for vulnerabilities discovered after the end of that support) and is a widely-used, popular operating system which has been in the public domain for many years.
These factors do make it more of a potential security risk than a newer OS that is actively supported by the vendor. At least with a newer, supported OS there is a better chance that a security hole will get fixed relatively quickly before it is exploited widely.
With regard to the other point you are absolutely correct. We should have rephrased this question to refer to “online accounts” rather than just “online banking” as not everyone uses online banking.
Many thanks for your comments.