Kohén és báálát tesuvá

These bring [bikkurim] but do not read the declaration:The convert, since he cannot say: “Which the Lord has sworn to our fathers, to give to us” (Deuteronomy 26:3). If his mother was an Israelite, then he brings bikkurim and recites. When he prays privately, he says: “God of the fathers of Israel,” but when he is in the synagogue, he should say: “The God of your fathers.” But if his mother was an Israelite, he says: “The God of our fathers’.

Rabbi Eliezer ben Yaakov says: a woman who is a daughter of a convert may not marry a priest unless her mother was herself an Israelite. [This law applies equally to the offspring] whether of proselytes or freed slaves, even to ten generations, unless their mother is an Israelite. A guardian, an agent, a slave, a woman, one of doubtful sex, or a hermaphrodite bring the bikkurim, but do not recite, since they cannot say: “Which you, O Lord, have given to me” (Deuteronomy 26:10).

Another major problem exists with implementing hafka'at kiddushin today. The Gemara records many objectionable marriages that are binding, indicating that the Rabbis do not annul them. For example, Chazal do not annul the marriage of a kohein and a divorcee, although such a marriage is explicitly prohibited by the Torah (Vayikra 21:7). While criteria presumably exist to determine when marriages may be annulled, the Gemara never articulates them. The Rashba (Ketubot 3a) provides some insight:

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Any priest who marries one of these three women - whether a High Priest or an ordinary priest - and engages in relations is punished by lashes. If he enters into promiscuous relations with her, he does not receive lashes for [violating the prohibitions against] a zonah, a divorcee, and a challalah. [This is derived from the fact that Leviticus 21:7 states the prohibition using the term:] "They shall not take." [Implied is that the prohibition does not apply] unless he takes - marries - [the woman] and enters into relations with her.

They shall not take [into their household as their wife] a woman defiled by harlotry, nor shall they take one divorced from her husband. For they are holy to their God

Based on the Oral Tradition, we learned that the term zonah used by the Torah refers to one who is not a nativeborn Jewess, a Jewish woman who engaged in relations with a man she was forbidden to marry, violating a prohibition that is universally applicable, or a woman who engaged in relations with a challal even though she is permitted to marry him.Accordingly, a woman who engages in relations with an animal, even though she is liable for execution by stoning is not deemed as a zonah, nor is she disqualified from marrying into the priesthood, for she did not engage in relations with a man. [Similarly, when] a man engages in relations with a woman in the niddah state even though she is liable for kerait, she is not deemed as a zonah, nor is she disqualified from marrying into the priesthood, for she is not forbidden to marry him.

Whenever a person has relations with an unmarried woman, even if she is a harlot who wantonly makes herself available to everyone, although she is liable for lashes, she is not deemed as a zonah, nor is she disqualified from [marrying] into the priesthood. For she is not forbidden to marry [the people with whom she engaged in relations].[When, by contrast, a woman] engages in relations with a man with whom relations are forbidden by a negative commandment that is universally applicable - the transgression is not specific to priests - or with whom they are forbidden by a positive commandment, she is forbidden to marry him, she is a zonah. Needless to say, [this applies if she engages in relations with a man] who is forbidden to her as an ervah, a gentile, or a servant.

Who is deemed a "zonah" [who is forbidden to a kohen]? Whoever is not a Jewess, or who is a Jewess that had sexual relations with a man to whom she is forbidden to marry in a generally applicable prohibition, or who had sexual relations with a "cholol" (the child of a kohen and a woman who was forbidden to the kohen), even though she is permitted to be married to this man. Accordingly, a woman who committed bestiality, even though she [is punished] with stoning, she does not become a zonah and she does not become invalid to a kohen, because she did not have sexual relations with a human. And a man that has relations with a menstruating woman, even though she is punished with kareth, she does not become a zonah and she does not become invalid to a kohen, because she is not forbidden to him. And similarly a man that has relations with a single woman, even though she is a lewd woman that made herself freely available, which is punishable with lashes, she does not become a zonah and she does not become invalid to a kohen, because she is not forbidden to him. However, a woman who had sexual relations with someone who is forbidden by a Biblical negative commandment, which are generally prohibited and are not uniquely [forbidden] to kohanim, or with someone who is forbidden by a Biblical affirmative commandment—and it need not even be said with someone who is forbidden by virtue of a forbidden incestual relationship—or with a non-Jew or slave, since she is forbidden to this person to marry, she is deemed a zonah. And so with a convert and a freed slave, even if she converted or was freed while she was less than three years old, since she was not a Jewess, she is deemed a zonah and is forbidden to a kohen. And so a woman who is subject to yibum (levirate marriage) with whom an unrelated person had relations, she becomes a zona. Some opinions say that one who has relations with one who is forbidden by a Biblical affirmative commandment or by a Biblical negative commandment—even the other negative commandments—she does not become a zonah except for instance in which one has relations with a woman subject to yibum.