Ummm, define realism?
With come exceptions, I generally prefer all of the fictional works I read or watch to be realistic.
By my standards, The Avengers was perfectly realistic (with maybe one minor issue in a fight scene that's not worth mentioning). Assuming, for a moment, that all the sic-fi stuff in the film is a thing that's real, then the movie's totality realistic. People act like people, situations develop the way they would, and things generally make sense.
The reason realism is important for someone like Batman is because he's a dude without super powers, and we're pretty familiar with what dude's without super powers are capable of. So, if a dude without super powers in a movie does something that dude's without super powers can't do, it's going to stand out and people will be taken out of the movie. If a movie has a more comedic or silly bent to it, then it's usually okay, but it tends to bug people in something that;s trying to be a straight drama with some action. So, it's a big deal. However, we've never encountered a super soldier or a Thunder God or a Hulk. They're not things that are apart of our daily experience. So if you put one in a movie, people tend to be more accepting of them doing weird stuff because we expect to not know how something with have no experience with works.
Similarly, the thing with Spider-Man and a more home-made looking costume. Yeah, people with Spider-Powers aren't a thing. So if they are a thing in a movie, whatever. But, people sewing clothes is a thing. Pretty much everybody who watches movies wears clothes, and most of them have at least a vague idea of how clothes are made. So, if we see a kid with no money making a costume, we have a preconceived idea of how that might look. It's why, at least in my case, the Raimi film costume bugs me. Some people will say "You accept people with spider-powers, but not that a kid could make that costume by himself." Well, yeah, I do. Because spider-powers is something the film is inserting into the world. But making clothes is a real thing.
So, generally, that's how I see realism being important. It's a super hero movie, we expect the movie to insert things that aren't part of a normal real world experience into the narrative. Where realism comes in is that a lot of movie goers expect the movie to not **** up the things that are real that we have preconceived notions of.