I shot the fake stuff for about 15 years until a guy opened a local M/L shop and stocked real B/P. Cleaning after shooting the fake stuff is no different than cleaning after shooting black, clean is clean. The main problem with guns that were damaged by the fake stuff is the owners didn't clean their guns properly or in a timely manner.
I have found from 50 years of shooting B/P stuff that John Q Publick doesn't know squat about cleaning a M/L. I shot Pyrodex, I cleaned and oiled my gun if I shot it. Back in the day we usually shot our rifles to empty them on the way back to the truck after dark and cleaned them when we got home. At the end of deer season, I would put my cleaned and oiled rifle up until the following year, I never had a speck of rust.
Shoot what you want to shoot, clean your rifle properly, dry and oil the bore before you put it up, you won't have any problems.
There are always a bunch of naysayers posting on this type of topic. All of you naysayers that shot substitutes then properly cleaned and oiled your firearm and still had the sub ruin your barrel, raise your hand and tell us about it.
I had a friend that wanted me to look at his gun, it wasn't grouping well for him, he shot Pyrodex. He had obviously shot his gun and put it up dirty although he claimed he had put his rifle up clean, NO WAY. I sent it to Bobby Hoyt for a re-bore.