By viewing them as a new continuity/history where events of past versions of history happened, but they don't happen exactly the same way, or even with the same chronology.
I mean the real answer is they don't care about coherency because DC's priority is to get money back by dangling familiar things to old fans, Snyder's priority is continuing his New 52 Batman lore, Jurgens priority is to bring back Post Crisis Superman, Rucka's priority is to bring back the familiar Wonder Woman, Johns' priority is to continue his New 52 Justice League lore (I think), King's priority is to do a character study on Batman (I think)... so they all kinda do their own thing... but if you want to try buying it, that's the closest thing I can sell.
To me, they matter if the present story relies on history. Like if they just move on and create stories set in the present day then I don't care, but if they started saying "5 years ago, a few days after my origin, I made a mistake that causes this villain to take revenge on me today, and it affected how I picked my sidekick" then yeah, it matters, coz now you bring it up, and you change history as I knew it, then I want to know what you changed.