Recent events in the news have raised the issue of religious freedom and specifically the legal implications of religiously focused face covering. The Constitution does give certain rights and freedoms that are relevant.
The "Fundamental Freedoms" section of the Canadian Charter of Rights and Freedoms states:
2. Everyone has the following fundamental freedoms:
(a) freedom of conscience and religion ...
A fundamental right to freedom of religion is a central part of the Constitution.
That said, all rights and freedoms are subject to reasonable limits prescribed by law that are consistent with a free and democratic society. The hard issue is where to draw that line.
The Supreme Court considered the issue of people who did not want their faces to be on public documents - drivers licences - in Alberta v Hutterian Brethren of Wilson Colony 2009 SCC 37. Here the Court held religious conduct was properly limited.
Alberta required all persons obtaining drivers licences had to have a photograph taken; a requirement objected to by Hutterites. Alberta conceded that the photograph requirement was a violation of the Hutterites' religious freedom but argued that this violation was allowable as a "reasonable limit" on Charter rights. The Hutterites maintained that the requirement was an unreasonable limit.
Chief Justice McLachlin, writing for the majority, found the law constitutional. She found that the government's need to fight identity fraud was pressing, and that driving was not a right, so the government was entitled to attach legitimate conditions to it.
A government requirement to reveal a face, contrary to a sincerely held religious belief, is valid but only if there is a substantial and important reason for the requirement and there is no other practical way to fulfill the requirement. Absent such basis a limit on freedom of religion will be held unconstitutional.