I just had the same problem, not sure if its related. Was a .dll file that the anti-cheat didn't like, said Untrusted system file? I have no idea what it is or means as I don't mess with anything. Seems to be a file extension. I copied the file to a folder, then deleted the file in question: ProgramFiles(x86)/OriginGames/Apex/paks/Win64/ui(01).dll. Restarted the game and it worked. There are a ton of files in that folder. Re-tested it again by putting that file back in the pak folder and got the same error.
I was playing this morning before the update and all was fine. Updated, and the game wouldn't load after splash and got that message.
Seems to be ok now although I just had 1 quick game in TDM.