That's what I thought, but I don't have the Google Play version installed.

First I tried installing Tasks from F-Droid, but it said the thing about the signature (even if Tasks wasn't already installed). So I went to Google Play and installed it from there, then uninstalled it, cleared F-Droid's cache and rebooted my phone. Still F-Droid tells me that there is no compatible signature.

I have several other apps installed via F-Droid, and I have never encountered that message when an app isn't installed in parallel.

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edit: added missing word