This word is acceptable for play in the US & UK dictionaries that are being used in the following games:

• Lexulous
• Wordscraper
• Wordosaur

n. Incongruity.

n. The state or quality of being incongruous, inharmonious, or inappropriate.

n. the quality of disagreeing; being unsuitable and inappropriate

"It enjoins its members to apply their own 'spin' in letters to the media, “highlighting the incongruousness of a major opposition party wanting to stay in the EU, whilst rejecting both the Constitution and the euro and then expecting to negotiate with 24 others on the repatriation of our fishing and farming policy”."

incompatibility   

irony