F-Droid is attempting to support reproducible builds--if you have a Debian system, you should be able to re-build the same .apk, or at least a similar enough .apk that the original package signature still passes.

That said, by my quick count, only about 18% of the F-Droid packages are reproducible right now.

    nokogiri https://verification.f-droid.org/ -e '$_.css("a").each{|a|puts a.text}'|sed -n 's/\.txt$//p'|sed 's/.*\.//'|sort|uniq -c