1. people or groups whose views, interests, or positions are so opposed that they cannot be brought into agreement or harmony
Usage: usually plural; often used in political or social contexts
2. things or ideas that cannot be made compatible or consistent with each other
Usage: usually plural; abstract usage

Examples

• The two political factions were irreconcilables, unable to find common ground on any major issue.
• Management and the union representatives proved to be irreconcilables in the labor dispute.
• Their irreconcilables differences made it impossible for them to continue working together.
• The irreconcilables in the debate refused to compromise on their core principles.
• Some saw freedom and security as irreconcilables that could never coexist.
• The irreconcilables within the party eventually split into separate organizations.