I think they ship prebuilt binaries, i.e. the exact same ones you find on the Signal website

AFAIK this also applies to Tor Browser, Orbot and other third-party apps distributed by Guardian

Edit: I downloaded the files and manually verified the signatures. They are indeed the exact same files.

Because I didn’t really know how to grab an APK from the Guardian F-Droid repo, I used their S3 bucket and downloaded the Signal APK. It’s named Signal-Android-website-prod-universal-release-7.30.2.apk, which is the exact same file name as the one of the APK you can get from the Signal website.

I then used keytool to print the signature certificate fingerprint: (renamed the files to make it less confusing)

keytool -printcert -jarfile signal-website.apk

Signer #1:

Certificate #1:
Owner: CN=Whisper Systems, OU=Research and Development, O=Whisper Systems, L=Pittsburgh, ST=PA, C=US
Issuer: CN=Whisper Systems, OU=Research and Development, O=Whisper Systems, L=Pittsburgh, ST=PA, C=US
Serial number: 4bfbebba
Valid from: Tue May 25 17:24:42 CEST 2010 until: Tue May 16 17:24:42 CEST 2045
Certificate fingerprints:
	 SHA1: 45:98:9D:C9:AD:87:28:C2:AA:9A:82:FA:55:50:3E:34:A8:87:93:74
	 SHA256: 29:F3:4E:5F:27:F2:11:B4:24:BC:5B:F9:D6:71:62:C0:EA:FB:A2:DA:35:AF:35:C1:64:16:FC:44:62:76:BA:26
Signature algorithm name: SHA1withRSA (weak)
Subject Public Key Algorithm: 1024-bit RSA key (weak)
Version: 3

keytool -printcert -jarfile signal-guardian.apk

Signer #1:

Certificate #1:
Owner: CN=Whisper Systems, OU=Research and Development, O=Whisper Systems, L=Pittsburgh, ST=PA, C=US
Issuer: CN=Whisper Systems, OU=Research and Development, O=Whisper Systems, L=Pittsburgh, ST=PA, C=US
Serial number: 4bfbebba
Valid from: Tue May 25 17:24:42 CEST 2010 until: Tue May 16 17:24:42 CEST 2045
Certificate fingerprints:
	 SHA1: 45:98:9D:C9:AD:87:28:C2:AA:9A:82:FA:55:50:3E:34:A8:87:93:74
	 SHA256: 29:F3:4E:5F:27:F2:11:B4:24:BC:5B:F9:D6:71:62:C0:EA:FB:A2:DA:35:AF:35:C1:64:16:FC:44:62:76:BA:26
Signature algorithm name: SHA1withRSA (weak)
Subject Public Key Algorithm: 1024-bit RSA key (weak)
Version: 3

The fingerprints are identical.

Another edit: I just noticed that Signal even has official instructions for checking the signature on their APK download page. They use apksigner instead of keytool, but it’s basically the same process.