In this case, it is not the MSM but the constituencies that are responsible for the dual standard. Republican voters tend to be law abiding citizens, and expect elected officials to live up to a certain standard. Democratic voters tend to be felons, dead people, conspiracy theorists, and illiterates, and they expect their elected officials to keep them entertained with anything outrageous and over the top.
I think the Repbublican rules came about after Dan Rostenkowski wouldnt resign after being indicted.
I also think they require being indicted for a felony to force resignation and I am not aware of any Democrat leadership being indicted since Rostenkowski.