Voltage appears on comparator input
You're relying on unspecified behaviour, so undefined behaviour happens. A floating input does exactly that: float. The tiniest influence can pull it anywhere.

Physically, opamps are chips, and there's bound to be some capacitive coupling between the inputs.

I also doubt you're able to actually measure the actual voltage: A multimeter typically has lower impedance (or at least in the same order) than a high-Z opamp input. In the case of an AD8611, the input bias current is lower in magnitude than -6 µA.

So, if you don't want an input to float, don't let it float. Use high-valued resistors to tie it to either ground or VCC, whichever level you prefer. Based on the -6 µA bias current, some 470 kΩ should work.

BTW, when building something like this, use a comparator, not an OPamp; while the same in theory, you can get latch-up behaviour with Opamps that you wouldn't see in comparators; also, comparators can be had for much higher bandwidths cheaply.

If you need a Schmitt trigger receiver, then use a Schmitt trigger receiver; LVDS receiver ICs do pretty much what you built.