Word for when something inappropriate or surprising is said or proclaimed in a jarring and nonchalant manner

. . . The person I'm addressing is obviously taken aback by the bombshell, while I, on the other hand, am behaving normally as if I hadn't said anything out of line.

bomb(shell) TFD

n. a stunning piece of news that is dropped without warning.

drop a bombshell (brick) TFD

To reveal something that is very surprising or unexpected.

Depending on the context and the needs of proper grammar, either idiom could be used.