Whenever a comic book character is cast there's usually some uproar. The recent anger about Robert Pattinson likely being the next Batman follows a long history of fans disliking a casting immediately. While I think the actors sometimes warrant healthy skepticism, many of these disapprovals seem to stem from an established image of the character they will be playing.
Batman in particular has gone through many stylistic changes over the years. He's been fun, serious, dark, angry, and every mood you can think of. His stories have been told in every possible tone and style. He's been reinvented multiple times. Through all this fans eventually develop an ideal version of the character in their minds,"My Batman". When Ben Affleck's Batman killed criminals, many were appalled. "This isn't my Batman."
I think that perspective loses sight of the varied history of these characters. Everyone has a different image of these characters in their mind. It's based on the stories you've read and your own personal interpretations. There is no definitive version of any character only different takes that build on a few core aspects.
This applies for any fictional character. It's almost impossible for an adaptation to please everyone. Instead of looking for our idealised version of the character we should instead embrace the unique takes for what they are. Who knows maybe "your Batman" will change.