Tosefta for Chullin 265:49

A Kohen who takes upon himself all the ritual obligations of the priesthood, except for one thing, we do not accept him. A Levite who takes upon himself all the Levitical obligations except for one thing, we do not accept him, as it is written (Lev. 7:33), "he who offers the blood of the peace-offering, and the fat [of the peace-offering] from among the sons of Aaron shall get the right thigh as his portion." [With reference to Kohanim (following Steinsaltz to Hul. 132b:15 to Hul. 133a:2)], I have only derived [that a Kohen does not share in the priestly gifts] only [if he does not believe in the validity of] sprinkling blood and burning of fats [on the altar]. How do we know [that they are also obligated in the rites of] the pouring [of oil onto the minchah-offering], the mixing [the ingredients together], the waving and bringing [the meal offering to the corner of the altar], the removing the handful and burning [on the altar], cutting [the neck of bird-sacrifices], receiving and sprinkling [the blood], the Sotah ceremony, the breaking the red heifer's [neck], and purifying the metzora [= leper], and the lifting the hands [to bless the people] inside and outside [the Temple]? As the Torah teaches (Lev. 7:33) "[among the] sons of Aaron," that is [to say] "all the rites" that are incumbent upon the sons of Aaron. Said Rabbi Shimon, you might think [lit. "it can be"] we don't prohibit them except from partaking in the priestly gifts within the Temple; how do we know [we also prohibit them partaking in priestly gifts given] in the countryside (see Y. Chal. IV.4.17)? As the Torah teaches (Deut. 18:4), "You shall also give him the first fruits of your new grain [and wine and oil, and the first shearing of your sheep]." Because [as it says, Deut. 18:5], "For the LORD your God has chosen him [etc.]"; thus, everyone who takes upon himself the service, he receives the gifts. All those who do not take upon themselves the service, he does not receive the gifts. During the time that the Kohanim do the will of [their Father in heaven, following the GR"A], what it says about them (Lev. 6:10), "I have given it as their portion from My offerings by fire." What is theirs, they take, and they do not take what is mine. And during the time that they do not do His will, what is said about them (Mal. 1:10), "If only you would lock My doors[, and not kindle fire on My altar to no purpose! I take no pleasure in you—said the LORD of Hosts—and I will accept no offering from you.]"