Christ is not a family name. It is a title that means 'the chosen one'. Christians give this title to Jesus because they believe God chose him to rescue people. Because the title is used for one person so often, English now handles it like a name. You will meet it alone, as in 'a follower of Christ', and inside 'Jesus Christ'. In this use it always has a capital C. In history, art and dates it keeps pointing at the same person.

This is a shout, not a statement about religion. It jumps out when something is hot, sudden, late or going wrong. It is spoken English, and it is strong. Because the word is a holy title for many people, some listeners hear it as misuse of that name and are hurt by it. So the same word can be ordinary in one room and offensive in the next. It often comes with 'Oh' in front of it. In writing it is usually followed by an exclamation mark or a comma, with the rest of the sentence after it.