Can I use PGP to sign a message without providing cryptographic non-repudation? The difference between a digital signature and a MAC is non-repudiation. A message with a digital signature proves that only the sender could have signed the message, whereas a message with a MAC proves that either the sender or the recipient could have signed the message.

Can an OpenPGP implementation, such as GPG, be used to sign a message without providing non-repudiation?

Please note that I am referring to non-repudiation in the cryptographic sense, not in the legal sense.
Yes, there's an indirect way to perform what's asked with PGP and variants.

Draw a an asymmetric public/private key (of a type that can sign), protected by a passphrase. Publish the passphrase-protected private key. Discard the public key (it's in the private key anyway). Use the passphrase as you would use a symmetric key: share it by trusted means between sender and receiver (perhaps together with the passphrase-protected private key). Generate, transmit and verify a detached signature (sig file) of a file to integrity-protect as you would do for a MAC of the file.