Is your name Kostic or Kostić ? There's one reason. The other is that typing out diacritics is a chore and people get what you mean without them anyway. Especially for programmers - we do most typing in English which doesn't use them, it's not in my "muscle memory".
I am talking about casual messaging - for formal writing you probably do come off as illiterate if you don't bother to use them.
Kostić but I use Kostic when I write English. If I use Serbian Latin (when I communicate with Croatians, for example) I would write down Kostić.
The problem with not writing out diacritics is that Serbian is a language with a fully phonetic alphabets. You don't need to ever guess how words are written or read. You lose greatest feature of the Serbian language if you don't use diacritics, when using the Latin keyboard. I shouldn't, ever, guess how a Serbian word is read when I see it.
My Norwegian teacher tried to tell me the same thing thirty years ago. For Norwegian it is manifestly untrue because pronunciation varies from valley to valley.
There are dialects but those dialects all use the same number of voices (one voice equals to one letter) so they can be expressed with the Cyrillic or the Latin script.
There are also regional accents but accents aren't different enough to pose any kind of problem when communicating.
Hell, even other language standards created from the Serbo-Croatian language aren't different enough to pose a problem when communicating. :)
For Polish (on computers) we have a keyboard layout called "polish programmer" widely adopted many years ago affectively making the original "polish typewriter" layout (that mapped diacritics to separate keys) almost extinct.
For typing diacritics AltGr is used (eg. ą = AltGr+a).
Typing without diacritics is considered clumsy at least within the groups of people I interact with.
On mobile it is a bit more relaxed, but the dictionary autocorrection is sort of OK. Conjugation, declension etc. complicates things, but you have the stem + most common suffix autocorrected, so usually it is a matter of erasing last 1-2 letters and changing them if needed. Also the Markov chain alike logic of autosuggestion quite often is right with the inflection.
I am talking about casual messaging - for formal writing you probably do come off as illiterate if you don't bother to use them.