How do I remove Outlook mail from Spotlight? I primarily use Mail.app for my Exchange mail account. But I need to keep Outlook around for those rare cases I need it (for instance editing distribution lists on the server).

But this makes Spotlight searches really convoluted. Every mail shows up twice. Is there any way I can disable the content from individual apps from being part of the Spotlight index? Or an obscure setting (I've looked) inside Outlook that disables Spotlight indexing?
You need to tell Spotlight not to search the Outlook Database on your local machine. 
Assuming you're using MS Office 2016 or later 
Here's how,


Open System Preferences > Spotlight
Click the Privacy Tab 
Locate your Outlook Database which can be found in the Library folder within you home folder. So /Users/userfolder/Library/Group Containers/UBF8T346G9.Office/
Drag the Outlook folder into the privacy tab you opened earlier within System Preferences.