To be fair, the parent post was clearly talking about Slavic languages, not "all the languages USSR forced cyrillic alphabet on", which were not Slavic and which required significant modifications to the alphabet.
Since we're talking about Serbian below, here are some characters from Cyrillic Serbian Alphabet:
Ђ/ђ
Ћ/ћ
Љ/љ
Њ/њ
Џ/џ
Ј/ј
Various diacritical marks, digraph, a jod... What makes this Cyrillic more unambiguous than the Latin equivalents?
Indeed: most notably, Croatian, Slovenian, Bosnian, Serbian and Montenegrin are all unambiguous with Cyrillic, but Latin script dominates, even in officially Cyrillic-first Serbia.
Again, it is seen as a political tool (pro-West or pro-Russia), when Cyrillic is technically better suited (there is certainly history as well, but that's very mixed up in the region).
Again, I am saying this as someone who has worked to implement things like full-text search, collation (lexical ordering/sorting) algorithms and tables, fonts and ligatures, functions like uppercase/titlecase/lowercase...
Eg. an already complex Unicode Collation Algorithm tables can never support exceptions with digraphs like "konjukcija" (nj is usually a digraph, but not here), etc.