People need to understand that as a Constitutional Monarch, the Queen has no choice but to sign this charter if presented to her by her government. She can only intervene in a case where the government is acting unconstitutionally - not just because it is doing something she may not agree with.
If the Church of England was opposed to the charter, she might have some method of protesting under her position as Defender of the Faith, but the Church of England and its Archbishops and Bishops approve the charter.