1.if a father says he a kohein bc he says his father was one, yet he himself is not shomer shabbos nor does he know of the responsibilities or restrictions of kohanim, and there are no other family members who are shomer shabbos who could testify for or against such a claim, is he and his sons considered to be kohanim, or is such a claim considered invalid? 2. If (one who considers himself) a cohen who was not raised religious but becomes shomer mitzvos later in life after he was married, must he retroactively inquire about his wifes status? If she openly admits to being considered a zonah given the criteria, must he then divorce her, even say after years of marriage and she’s just finding out about these requirements now?
If the father is knowledgeable about his Jewish background, he is generally believed that he is a kohen, and accordingly, the son is, as well. If the couple involved is already married, the kohen husband should definitely not ask his wife about her previous relationships with gentile men. Even if she volunteers this information, he may not believe her. That being said, R. Moshe Feinstein, the late leading authority in America, says that being that the kohen often has reason to doubt the veracity of his non-religious father’s or grandfathers’ relatively unqualified testimony on the topic, and also, there is reason to believe that his mother or grandmother, who also were non-observant Jews, may have had intimate relations with a gentile man, in that case, we would relate to the man, his wife, and his children, as regular Jews, and not kohanim. With love of Israel, Rav Ari Shvat