Is it possible to allow CSV downloads of chart data while disabling "Show Detail" and "Interactive Chart" for content published on the server?

Yes, it is possible.

Access the published content and click on the settings button (the “…” in the upper right corner of the screen), then select "Setting."

A setting dialog will appear, where you can disable “Show Detail” and "Interactive Chart."

Once these settings are applied, users will be able to download chart data as a CSV file while “Show Detail” and “Interactive Chart” remain disabled.