Her Majesty is the Defender of the Faith, which means a defender of faith in general, and not of any particular religion (as Canada has no State religion or faith). The Queen’s roles and titles in other countries (including the United Kingdom) have no effect on the Queen’s constitutional role here. The Queen’s title in Canada, per the Royal Style and Titles Act, is:
Elizabeth the Second, by the Grace of God of the United Kingdom, Canada and Her other Realms and Territories Queen, Head of the Commonwealth, Defender of the Faith. As far as our constitutional arrangements are concerned, the Queen’s role as the Supreme Governor of the Church of England does not exist. As Her Majesty acts in Canadian affairs only on the advice of Canadian ministers and advisors, and within the bounds of our Canadian constitution, this is entirely a non-issue.
Members can dramaticise this as much as they’d like (for example, s_lone suggesting that those who respect the Queen are spineless, or dumpthemonarchy suggesting that the Queen’s personal religious convictions undermine Canadian democracy), but at the end of the day, Her Majesty the Queen of Canada has always acted in the most admirable way possible as our head of State. Our unique take on constitutional monarchy has served Canadians well, and we should continue to cherish a system that helps to safeguard — for so modest a cost — fundamental principles of democracy, such as responsible government.