John, your correspondent has a good point (as you recognize), and, as you say, the same applies in England. For example, with the exception of “hatches, matches and despatches” and, when the time comes, my own deathbed conversion, I never step foot inside a church, but I always describe myself as C of E.
The more interesting question is how much the distinction between ‘cultural’ and ‘actual’ religion really matters in practice in countries where the wilder excesses of religious enthusiasm have, thank God, faded away. If, in such countries, you identify yourself as a cultural ‘Christian’, your general worldview and moral outlook are, if only loosely, likely to reflect the way that that the practical teachings of that religion (who cares about theology?) have evolved in that country and will not be particularly affected by, for example, your view as to what may or may not have happened two thousand years ago.
What is more problematic (I seem to recall this was discussed in ‘The Closing of the American Mind’) is whether this cutural Christianity is strong enough to be passed on to successive generations. I’d argue that it is, but only in societies culturally self-confident enough to do so. Sadly, England no longer appears to meet that test.