As someone who has spent significant time in non-Christian religious contexts in the West, I affirm that yes, it's possible to live in e.g. London and need to be closeted about one's Christian beliefs and/or religious identity. The privilege that Christianity has in general in the West does not mean that there are no contexts in which it is contentious and/or risky for an individual to be out as Christian.

(I would be interested in knowing more of your backstory, but not at cost of unease for you, and certainly not as some kind of justification for your use of the term "closeted".)