The MCU movies are not considered campy by most standards since they take themselves and their internal universe completely seriously.
Batman of the 1960s was campy. The Flash TV show is campy. The MCU may have some humorous moments but the tone, overall, is serious and thought-provoking. Civil War, Black Panther, Winter Soldier, and Iron have all been mentioned here already but you can go on and on with those films.
Okay, but using such a strict bar for campiness also invalidates the original claim. There are plenty of superhero renditions that don't qualify as campy that predate the recent wave and the technology that supposedly enabled it. (eg Burton's Batmans).
No it doesn't. The Tim Burton movies were also campy and they reveled in it. Also, the point isn't about whether the movies are campy or not but simply that we're at the point where you can show superheroes on screen believably. Even Burton's Batman had to use fake penguins and matte paintings to try and make Gotham seem real and it still looks wooden and lifeless.
I would say that Raimi's Spider-man (though not fully) and Nolan's Dark Knight Trilogy pushed us into the age of superhero believability and popularity.
It's the difference between Lou Ferrigno being painted in green makeup lifting up cardboard and foam vs. a fully realized Hulk that matches what was originally in the comic books in ferocity and strength.
Not by those standards but, by believability and realism standards, it definitely is. The difference is that the Flash TV show is one of the shows that knows exactly what it is and when it's campy and it leans into that instead of trying to play it straight.
Batman of the 1960s was campy. The Flash TV show is campy. The MCU may have some humorous moments but the tone, overall, is serious and thought-provoking. Civil War, Black Panther, Winter Soldier, and Iron have all been mentioned here already but you can go on and on with those films.