The airplane argument doesn't fly [pun intended]. You aren't allowed to bring protractors, metal forks, or even toe-clippers on an airplane. Shall we ban protractors from geometry classes and metal forks from school cafeterias?
Point taken on the separation of church and state. In practice we have a secular government. Tangentally to the kirpan issue though, having an official religion "on paper" doesn't mean there isn't a de facto separation of church and state. I realize that's a bit of a weird concept, but no weirder than the our head of state happening to also be the Australian head of state.
Yes, the Canadian head of state happens to be the same person as the Austrailian head of state, the New Zealand head of state, the Scottish head of state, et al. and the person who holds this title also is the monarch of England, who also happens to hold the title as the head of the Church of England, and, incidently (by a quirk of history) also holds the *Catholic* title of "Defender of the Faith". But this holds no sway over who can and cannot be elected to parliament or appointed to the senate, it's more a peculiar artifact of history than anything else. Québec's official Catholicism is an equally impotent bit of history. It was concession made my Imperial England, along with other cultural allowances because, basically, once New France was conquered all England really wanted was taxes to fund wars in other "problem" colonies, not another problem.
We have, in pactice, a secular government. A nation that does not have a separation of church and state in practice does one or more of the following: requires membership in the state religion in order to hold office, confers or denies citizenship based on religion, or grants legislative power to clerics simply by virtue of their religious authority.
Canada: home of the hard-to-understand, not-quite-complete, lip-service-to-history way of doing things. For example, did you know UBC is a fiefdom?