Linux and online purchasing/finances

Is there any merit to strictly limiting online financial interactions and management of accounts through a Linux OS?

Why/why not?

When you perform high risk or high value activities you can mitigate the risk by having a separate security domain. Here you are suggesting a Linux OS as a more secure separate security domain. All things being equal yes you are less at risk using an operating system that is attacked less. Why? because Linux is simply much less targeted plus you are creating a separate security domain isolating attacks from your main platform.