Could the interaction between photons and intergalactic matter cause the cosmological redshift?

This is actually an old idea that dates back to the 1960's. The answer is NO. There is not enough intergalactic matter to 'redden' the light from distant galaxies. More importantly, intergalactic matter would not produce a spectral shift in the incoming atomic lines from distant galaxies in any way that resembles the Hubble Law.