Related for Zevachim 34:5

There is a greater stringency with regards to consecrated food [of sacrifices] and Terumah than with regards to the [waters of] purification [containing the ashes of the red heifer], since everyone is believed regarding [the purity status of the waters of] purification, but not everyone is believed as to [the purity status of] consecrated foods or Terumah. There is greater stringency with regards to the [waters of] purification, which is that one who is pure [with respect to the waters of purification] is impure with respect to consecrated food and Terumah, and there is no than with the purity of consecrated food and Terumah. There is a "counting" with respect to consecrated food and Terumah (i.e., 3rd- and 4th- level impurity, see Minchat Yitzchak), but there is no "counting" as to the [waters of] purification. A mourner is forbidden [to partake] in tithes but permitted [to partake] in Terumah and in [the purification rite involving] the red heifer. A tevul yom (i.e., one who has immersed but remains impure until sunset) is forbidden in Terumah but permitted in tithes and in the red heifer. One who lacks atonement (i.e., who has not yet brought a sacrifice) is forbidden in the red heifer but permitted in tithes and in Terumah.