Answer:
It depends on the context of the sentence. Right now there is too little information based on that one sentence.
The word "irreconcilable" is used when in relation to humans' disagreement of / inharmonious feelings. It is usually used for human relationships which are unable to be fixed/mended. If I were to reconstruct ur sentence to make the meaning of the word "irreconcilable" more related, I'd put it this way: "The mistake he made caused their friendship to be irreconcilable." Note: A mistake though, is not irreconcilable. Hope I've helped.