The Night's watch conspirators believe Jon broke his oaths because he opened the gates to the Wildlings who had been their enemies.
But the oath, as Jon pointed out, is to protect the realms of men and the Wildlings are men. They had forgotten their real enemy. I don't think we can say that show Jon was an oathbreaker knowing what he know of him.
Unless we're talking about that time he ran away for like 5 minutes and the other Night's watch brought him back.
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