Exporting sections of an outline is something we will be considering adding an ability for in the future.
However, if your document is in such a way that you can hide all the confidential info by collapsing that section, you can collapse all but the pertinent section and then when you export to some format, you will only see the exposed text. The formats you can export to for this would be Plain Text, RTF, RTFD, HTML (only the 'HTML' option, not dynamic or any others), or you can go Print -> Save to PDF.
And just a reminder, if you want to make an official feature request, please send an email to
omnioutliner@omnigroup.com
Thanks!
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Derek M.
Support Ninja
The Omni Group