Zavim, chapter 3, mishna 2, lists a bunch of cases in which someone is deemed tame (ritually impure) by decree of the rabbis. However, it concludes,
וְכֻלָּן טְהוֹרִין לִבְנֵי הַכְּנֶסֶת וּטְמֵאִין לִתְרוּמָה
This means (as explained by the commentaries there) that the decree only goes so far as to bar the person from eating t'ruma: he can eat regular, secular food, even if he is the sort of person who always eats such food while not tame.
I'm wondering about the term used to describe such people, "בְּנֵי הַכְּנֶסֶת", roughly "people of the assemblage". Why are they called that?