Rav Eliezer Waldenberg (author of Shu"t Tzitz Eliezer) in Nishmas Avraham Even Ha'ezer, p. 252 (points he wrote in response to the Nishmas Avraham (note this is in the first edition, I'm not sure it is in the second edition, or it may be incorporated into the text and not be an appendix)
3. E"H Siman 2 - Nishmas Avraham discusses needing to inform [the other party] (or disclose) about a family blemish or psul, or if the father is a non-Jew (and the mother is Jewish). From Yevamos 45a when Rav Yehuda told him to either marry a woman like himself (of a Jewish mother and non-Jewish father) or go to another place [and not disclose your father is not Jewish), and Rava told him to disclose it or marr ya woman like himself. Nishmas Avraham quotes my dear colleague R' Shlomo Zalman Auerbach asking on this, "is there not a transgression of onaah not to disclose that his father is not Jewish, even though the child is completely kosher?"
To my understanding, it is a problem of onaah [not to disclose it]. If the second party would take the first party to a din Torah [for not disclosing] they would find a sympathetic ear. The advice in Yevamos was only to show that to marry such a person is allowed: even though they ruled it is permissible, people will not agree to such a match. In a place where they won't aks him about his background, since they are not obligated to [see Beis Yosef and Tur Yoreh Deah 268) he may marry a completely Kosher woman (meaning both her parents are Jewish). The Gemara there was not concerned about the prohibition of onaah [and it was partially because of a temporary injunction due to extreme hardship (horaas shaah) in order to publicize the psak that someone whose father is not Jewish [but his mother is] is allowed to marry a kosher Jew, despite the public not accepting this lenient ruling...Even if we use this Gemara in Yevamos as a heter to himself [not to tell if he wasn't asked] we cannot learn a heter to others who know about his background; they must disclose it, especially if they were asked.
That which the Halacha is that the child of a non-Jewish man and Jewish woman the children are Kosher (not mamzer) but they [female offspring] are blemished and disqualified from marrying a Kohen as Shulchan Aruch paskens (EH 4:5 and 19), it certainly must be considered a serious blemish. They, and the person himself (ntoe the male offspring of such a union) is required to siclose this to the other party. Maharsha and Chemdas Shlomo require such a person to require Gerus (see out multiple posts on this subject), as Pischei Teshuva cites, and Rav Shlomo Kluger in Tuv Taam v'Daas YD Mahadura Kama 229, that woe to us to give him a Jewish name before conversion. Despite that the majority of poskim do not agree [that such a child requires conversion] as the Otzar Haposkim mentions, nevertheless I mention this to show the blemish of such a person, that even though we don't require conversion, [we do pasken that] such a girl is disqualified from marrying a Kohen.
It is worthwhile to point out that a convert must disclose thiat fact [that they are a convert] to the second party. For we find (Berachos 8b) that Rava instructed his sons not to marry converts, and R' Yaakov Emden in Haghos Yaavets there that one reason is that descendents of converts will have some impression from their source (non-Jewish ancestor) and this reason applies to the son of a non-Jewish father as well. This is also seen from Pesachim 112b that Rabbeinu Hakadhos instructed his sons likewise. Also see Haghos Yaavets Horios 13a. We can also add a reason: the shechina only dwells on meyuchas families, as Tosfos cite in Niddas 13b and Yevamos 47b, and this also applies when the father is not Jewish.
Shu"t Mayim Rabim 9-10 (perhaps this link) cites this in practice (l'maissa) to break an engagement, that the bride's side informed the groom's side that the brides parent were converts was enough of a blemish to break off the engagement.