The phrase ceteris paribus has a Roman historical context mainly related to the law and to legal and political debate. It entered English usage via mediaeval people, often monks and/or scholars, who were themselves fluent and literate in Latin. Its use suggests that the judgement, belief or plan under discussion is proposed or made on the basis of the evidence provided and assuming that there is no other factor either unknown or with-held that might cast doubt upon it. In this context, it is a standard expression. As time has gone on it has often come to be used as a sort of verbal tic in the attempt to appear professional and judicious.
The English language does not have the grammatical inflection of Latin and so the literal phrase other things equal ('on a par') doesn't sound right. The participial being is the best solution. The use of the -ing) participle here has, as the Latin can, have a causal sense or a conditional (if) meaning. Other things being equal works the same way.
Does this make it just grammatical usage, or is it an idiom? One test is to see what other languages do with these relationships. There is a wide variation.
Greek: Αλλα πραγματα αν ειναι ισα [If other things are equal - but literally 'other things if they are equal']
Italian: aparita di altre condizioni (on equality of other
conditions)
French: toutes choses etant Egales par ailleurs - Everything <lit: all
things being equal otherwise>.
German: unter sonst gleichen Bedingungen - Under otherwise equal conditions
The German phrase is, not surprisingly more distant than the other three from the phrase in question, but retains the idea of equality/sameness or equivalence.
More fluent speakers of German or French or Italian than I may differ. However, I think it is fair to say that there are at least some differences of idiom in the sense that literal transliterations of them into English come out clumsily or with a difference of emphasis, which could be described as idiomatic differences. Perhaps you could think of the expression as a sort of speech habit, seeking to convey the exercise of due and honest caution.