Chapter 25 of Masechet Keilim deals with the distinctions between insides and outsides of vessels with regards to tumah coming from tamei liquids, which is Rabbinic. If a vessel's exterior becomes tamei from tamei liquids, we say that its interior remains tahor; this makes it obvious that this is Rabbinic tumah.
In mishnah 25:9, we see that this distinction doesn't apply for vessels used for kodashim:
כְּלֵי הַקֹּדֶשׁ אֵין לָהֶם אֲחוֹרַיִם וָתוֹךְ, וְאֵין לָהֶם בֵּית צְבִיעָה.
Utensils used for holy things do not have reverse side and interior, and do not have a finger-hold. [from Kehati]
דהנוגע באחד מהן כנוגע בכולו.
Since for one who touches one of them [the outer side, inner side, or finger-hold], it's as if they touched the entirety [of the vessel].
Thus, vessels used for kodashim don't have the benefit of a distinction between their outer and inner sides to remind us that the tumah of liquids is Rabbinic.
Why would we be more stringent with regards to vessels used for kodashim than other vessels, since we make it more likely that we will (accidentally) burn kodashim that is Biblically tahor (but Rabbinically tamei).