The White House and the Trump Campaign turned over millions of pages of documents requested by Mueller. Many, probably hundreds of thousands of those are privileged. Some of the information in the report is almost certainly privileged information the WH has legitimate authority to withhold under Executive Privilege. They cooperated with Mueller in good faith. I would expect the WH will review the report before it's release and direct Barr to redact as appropriate.
Of course, Trump may be perfectly happy to have the report, which does exonerate him by what it does not contain, released. Letting the Left go balls to the wall to demand its release would just play into his hands.