MO is whatever anyone who self-declares as MO wants it to be. There was no founding movement with MO, as there was with Chasidus, the Mussar movement and even illigitimate movements like Reform and Zionism.
To some MO means mixed swimming and TV. To others it might mean Torah Umadda. To other MO folks, they reject even that. Since there never was a movement that got together and said “lets start a MO movement” as occured with the other movements I mentioned, there is no authority that can say no, your philosophy is wrong and not MO. Instead, when asked how can you can allow mixed swimming (for example) in your bungalow colony, the answer invariably is “oh, we’re an MO colony.”