Microsoft has a lot of great engineers that have no religious bias against Linux. This was strictly a Bill Gates/Steve Ballmer thing. The smartest thing Nadella did was get rid of the Windows religion aspect to their work and let their engineers do the best thing, and not be afraid of Linux.
I doubt that has much to do with "religion"; they simply don't think a Linux version of Office will bring in enough revenue to be worth the development and support costs... and I probably wouldn't disagree with that assessment.
Linux has large (majority?) market share in the server and IoT markets, but a very tiny market share when it comes to desktop.
I think that's a pure business decision, they have Office for Android and iOS. Office for Linux might not make that much sense given the low market share on client - but Office 365 has most as WebApps anyway also.
You can run the web app in your browser. It's no different than what Google does with ChromeOS. A fully capable web app. I haven't used it in a while, but on the feature front the only place it seemed to lag was collaboration, but I think even that is now on par with Google.
