That quarks have charge, means they participate in electromagnetic interactions. So they can absorb, emit, & scatter photons.
It doesn't matter that a neutron is overall charge neutral, because it's the elementary particles that make up the neutron, that participate in interactions.
This is why, you don't fall through the earth, despite being made of charge natural atoms, because the surrounding electrons of our atoms repel those of the atoms making up the ground, counterbalancing the gravity pulling us down.
However we have for example Neutrinos which are weakly interactive even more so than the photon and are not baryons (the real reason why neutrinos are not a baryonic DM candidate ;)).
A neutrino will not interact with a photon at all since photons do not have an interaction through W and Z bosons (both W, Z and Photons are electroweeak gauge bosons) and neutrinos are not charged.
There are a lot of reasons why you wouldn’t fall through the earth electromagnetism is just one of them, however even non charged baryonic matter can be “solid” and resist gravity for example neutrons will resist gravity through degeneracy it’s all a question of which type of interactions are possible.
There is much more to particle interactions than charge.
As far as photons interacting with neutrons, neutrons while being neutral in charge have a magnetic diepole which is why the photon can couple with them.
You can make baryonic matter that is massive and does not interact well with photons, the LHC has been making some new baryonic matter but none of it is a good candidate for dark matter so far.
But overall yes currently it looks like baryonic matter at least the one of the standard model without any extensions produces isn’t a good candidate for DM.
If you drop some neutrons on the ground, they will go through the ground some short distance until they interact with something, most likely via the weak interaction.
Photons do scatter off neutrons due to various effects, but the cross-section is really very low. I haven't checked the numbers, but I suspect that it's more than low enough that this type of scattering does not rule out neutrons as dark matter. (Plenty of other things do rule out neutrons as dark matter.)
The reason you don't fall through the ground even though you have almost no net charge has nothing to do with quarks.
Think the main reason neutrons are ruled out as DM because free neutrons decay, they have a
half-life of ~10 minutes. So if DM was neutron, nearly all of it would have decayed into protons, electrons & neutrinos, the former two of which we would definitely be able to see.
Baryonic matter doesn’t have to be free neutrons, cold baryonic matter can be stable we have found it already just as we have found brown dwarfs there just isn’t enough of it to make up for the missing mass hence it’s not a likely candidate at this point.
