Well, if by 'rule' you mean 'instructions that must be obeyed' - yes.
There are certain apparently unbreakable rules such as the one about ending a a non-emphatic, affirmative sentence with a full stop (period), though we do have the annoying problem that it appears to be impossible to find a definition of the word 'sentence' that satisfies everybody. If we can't define 'sentence', how can we always be sure about where to put full stops?
The various manuals of style disagree on many points. The 'rules' of any one may be regarded as absolute - by the publishers who accept them as absolute rules; they may be accepted as good advice by others. That's all.
"Use a semicolon between independent clauses that are not linked by any transitional word or phrase." Fine - but what is a transitional word? The first site I looked at one minute ago listed 'namely' and 'that is' as transitional words/phrases (
Writer's Web: Transitional Words and Phrases). If that site is correct, then presumably we do not need to use a semi-colon when these words link independent clauses.