The reason most people are refusing to accept the death of Dmitri is that he was built up far too much to end up as a minor character with the main purpose of being killed off. And it’s true that Dmitri was given a lot of personality development during the show so far, to the extent where he was very much a major character.
With that in mind, it definitely would not be a standard move for the producers to take him out so suddenly and without any true closure to his story. It’s not how most shows would handle that, in the least.
But then again, this is “Madam Secretary”, and the production has shown multiple times that it does not take a “standard” approach to its plot development. It’s possible that the producers intentionally handled the character in this way in order to make his sudden death even more dramatic.
But if that’s the case, they should at least introduce someone else to take his place, as he did occupy a relatively major position in the story. Will this be a new character, or are we going to see a new side to someone we already know? Only time will tell for sure, but both are equally possible given the history of the show.