Could an OPAMP have different input resistances for +/- inputs? Would that be a problem?

for bipolar opamp, you will see input resistance, but for cmos opamp, ideally, the resistance approaches infinity. in reality, due to the esd, cmos opamp also has a resistor in the range of 100M ohm.

It is true that in closed loop the input resistance might be different in the + and - inputs, but only for single ended configurations.
For fully balanced opamps both inputs have the same circuit connected to them, and due to the balanced nature of the circuit, the input resistance for both of them will be ideally identical, the same way they are under open loop conditions.

Concerning MOS inputs, the input resistance will be almost infinite but only at DC. At higher frequencies the unbalance will be noticeable again only for SE topologies, while for FB configurations they should be identical.

Best
Tosei