It looks like the only thing preventing Tutanota's Android app from being built reproducibly by F-Droid is a minor sort order issue when assembling Javascript files. Perhaps it is related to JS minimization:
https://verification.f-droid.org/de.tutao.tutanota_342020.apk.diffoscope.html#assets-tutanota-dist-index.js

Once that is fixed, then it would make sense to use Briar Project's sorted filesystem hack to get a fully reproducible build:
https://gitlab.com/fdroid/fdroiddata/commit/7fb7bec3ec1c214500148962959229b7c2b203f6

Also, FYI, we're putting together a blog post about privacy messaging, reproducible builds, and F-Droid where we also mention Tutanota. Here's the draft:
https://gitlab.com/fdroid/fdroid-website/merge_requests/359