Related sur Haguiga 3:9

One who immerses one of them (i.e., his hands), and prepares tahorot (i.e., food that must be prepared while in a state of purity): All the tahorot that he [attempted to] prepare in a state of purity before he immersed both of them are [deemed] impure, since one hand renders the other impure to thereby render the consecrated food impure, the words of Rebbi. Rabbi Yosei son of Rabbi Yehuda says, [the rule should rather be formulated as,] "to render the consecrated food disqualified."

One who immerses one of them (i.e., his hands), and prepares tahorot (i.e., food that must be prepared while in a state of purity): All the tahorot that he [attempted to] prepare in a state of purity before he immersed both of them are [deemed] impure, since one hand renders the other impure to thereby render the consecrated food impure, the words of Rebbi. Rabbi Yosei son of Rabbi Yehuda says, [the rule should rather be formulated as,] "to render the consecrated food disqualified."

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.

If tax collectors entered a house and wrote on the outside [that] everything that is in the house is [ritually] pure, they are believed as to the purity of [articles involved in] the purification rite [of the red heifer], but they are not believed about the purity of Terumah, and in Jerusalem they are believed as to the purity of all the consecrated utensils but not about Terumah, and during the season of the pilgrimmage festival, [they are even believed] about Terumah. One who buys utensils from am ha'aretz skilled craftspersons, and one who sells utensils to am ha'aretz skilled craftspersons are believed about the purity of [articles involved in] the purification rite, but are not believed about the purity of Terumah.

If tax collectors entered a house, the house is unclean. If a Gentile was with them they are believed if they say, "we did not enter" but they are not believed if they say "we didn't touch anything." If thieves entered a house, only that part in which the feet of the thieves have stepped is unclean. And what do they cause to be unclean? Food and liquids and open earthenware, but couches and seats and earthenware that have tightly fitting covers remain clean. If a Gentile or a woman was with them, all is unclean.