You mean, specifically Christianity? Even though I am repeatedly implying all religious groups?

Anyways, “ethnic group” may have been poor choice of word, but it is used by some religious people to call themselves that:

An ethnoreligious group (or an ethno-religious group) is a group of people with a common religious and ethnic background[1] or, in some cases, a religious background exclusively.[2][3]

Read citations if you want: en.wikipedia.org/wiki/Ethnoreligious_group