Pidyon haBen

Usually halacha treats certain areas as dinei mamonos - financial law, and other areas as issur v'heter - ritual law, and the rules for the two areas are often very different. Pidyon haben is a gray area - do we treat this like terumos and ma'asros, where there is an obligation to separate and distribute a % of one's crop to a kohein as a ritual obligation to make the food edible, or is it purely a financial obligation? One possible difference is raised by the Minchas Chinuch - one an forgive a financial obligation and remove a debt (mechila), but one cannot remove a ritual obligation by forgiving payment. A kohein has no power to forgive the payment without accepting anything, which would seem to indicate that this is a ritual obligation. The Tzemach Tzedek discusses a case of a woman who gives birth and does not know whether her father was a kohein or levi (which would remove the obligation of pidyon haben). The halacha is "ain holchin b'mamon achar harov" - we do not follow majority in laws of mamonos. Even though if we follow the majority of people we would assume the father is a yisrael and hence there is a pidyon obligation, the tzemach tzedek rules that we treat this as a financial matter and no obligation exists. The Kuntres haSefeikos (6:5) argues. There is much more to discuss on this issue!