Yep, I just set the P2 device type to None.
Tested it using MVS Asia/Eur v.6, USA v.5, and Japan v.6 BIOSes with: Cyber-Lip, Spin Master, Sonic Wings 2/3, Magician Lord, Last Blade 2, Samurai Shodown V Special. Every single one of them exhibits this behaviour.
Just tested it with KoF94, also can't add coins.
Grabbed my laptop (never had a RetroArch on it), downloaded a fresh copy of RetroArch (64bit). Installed the FBN core, copied neogeo.zip BIOSes to System/fbneo. No other changes. Dropped kof94.zip onto it. Pressed Right Shift. Coins add just fine. F1 -> Controls -> Disabled P2 input device. Pressed Right Shift. No more coins get added.
I'm at my wit's end.