First, thank you for actually giving a comperhensive and seemingly honest answer for a change. It is a refreshing change from your usual approach.
Let me repeat your words, with the change you suggest of replacing "ironic" with "disrespectful":
My point is that it's disrespectful to envision someone railing against the Bible at home, then going out somewhere and singing: GOD SAVE THE QUEEN.
Disrespectful to whom? The Queen is a figurehead, the national anthem (of the United Kingdom, not the national anthem of Scotland) is a a jolly, rousing tune that, like many national anthems, allows one to express ones sense of patriotism, typically in company with others. The words are incidental, a fact reflected in the inability of most Brits to recall what the words are. (And of course some verses have been set aside, such as the one that includes the words "rebellious Scots to quell". ) Singing the UK national item neither represents admiration for the Queen, or belief in God, but simply - as noted - an affection for ones homeland.
It's equally disrespectful to envision someone driving past his nation's flag with a cross on it, on his way to an atheist convention.
In the 2011 census 53% of Scots identified themselves as Christians, down from 65% just ten years earlier. I would be astounded if the 2021 census did not show a figure below 50% and this is setting aside the fact that a proportion of those identifying as Christians are so in name only. In short, Scotland is no longer a Christian country, while the religious connotations of the flag have been subsumed in its value as a symbol of Scottish patriotism and, in some cases, of the desire for full independence. So there is no disrespect involved.