The people going with the narrative that this is motivated by Deadpool are foolish and gullible.
DC made it clear that they're going for the "hard PG-13" stamp as the consistent tone of the DCCU, and Snyder is a guy who revels in his styilized ultra-violence. It was only to be expected that the film got trimmed in some fashion, I mean, just look at the action in the trailers and Man of Steel, this ain't your grandma's Superman.
Not to mention the time it takes to edit a cut of a film, submit it to the MPAA, have it go through proper review and rating, and then having it finalized. This was in the works long before Deadpool released.
It's a smart move, going for this approach of hard PG-13 and R on home video. I'm a big fan of the darker and more fucked up and violent DC comics, and I can't wait to see the brutal Batman and R-Rated Suicide Squad in action when these roll around to the home market. In the meantime, I'll enjoy the "fun for all" cuts in the theaters.