This question has been directly addressed by the paper The Mechanism of Proton Exclusion in the Aquaporin-1 Water Channel. I think it's a pretty good one too! I paste the abstract below:
Aquaporins are efficient, yet strictly selective water channels.
Remarkably, proton permeation is fully blocked, in contrast to most
other water-filled pores which are known to conduct protons well.
Blocking of protons by aquaporins is essential to maintain the
electrochemical gradient across cellular and subcellular membranes. We
studied the mechanism of proton exclusion in aquaporin-1 by multiple
non-equilibrium molecular dynamics simulations that also allow proton
transfer reactions. From the simulations, an effective free energy
profile for the proton motion along the channel was determined with a
maximum-likelihood approach. The results indicate that the main
barrier is not, as had previously been speculated, caused by the
interruption of the hydrogen-bonded water chain, but rather by an
electrostatic field centered around the fingerprint Asn-Pro-Ala (NPA)
motif. Hydrogen bond interruption only forms a secondary barrier
located at the ar/R constriction region. The calculated main barrier
height of 25-30 kJ mol(-1) matches the barrier height for the passage
of protons across pure lipid bilayers and, therefore, suffices to
prevent major leakage of protons through aquaporins. Conventional
molecular dynamics simulations additionally showed that negatively
charged hydroxide ions are prevented from being trapped within the NPA
region by two adjacent electrostatic barriers of opposite polarity.
The difference between glycerol and and a protonated ion such as H3O+ is charge, and many ion channels are selective based on charge too. Of course, other properties play a role, such as size and steric shape, but charge is a very important one and this applies to a great many channels beyond aquaporin!