Last year we went to DCA until around 2:00 on the actual 4th, and it wasn’t too bad at all!
That doesn’t really mean anything predictable for this year, but it’s encouraging? We spoke to a few people who were visiting and said it hadn’t been too bad prior to the 4th, either (which lines up with PP’s experience).
The “conflicting information” makes sense because there’s really NO way to know, though. Crowds could be miserable; crowds could be manageable or even nice... with Pixar Pier opening on June 23, it’s possible that people will plan their trips for after that, which may concentrate the crowds a bit more towards the 4th compared to last year (when people were waiting for Fantasmic! and the railroad to open later in July). But things like weather factor in, too... lots of variables.
I’d expect big crowds, but with planning and good attitudes, I’d say you could still have a great time. And those crowds certainly might not materialize, or they might not be consistent.