Well, I did that thing, long ago. When I joined the army, it was a requirement, and I swore and signed an oath of allegiance to the Queen as head of the armed forces. It never caused me any loss of sleep. Nor did the fact that I lost the right to vote, being a soldier.
Later on I embraced republican ideas (that's English, not American, republican) But there is a lot to be admired about a benevolent monarchy. You don't get daft presidents, for one thing.

I would swear an oath of support to a country, but not to a head of state, now.