I fully endorse your objection to exemption from human rights legislation for the churches. Why should Christians have any problem with upholding human rights?
My ancestors in the Faith decided some centuries ago that in things that affect obedience to God, the Church (note the big C, which means the whole lot) is not subordinate to the state.
Nonetheless, where the state is doing its job of serving God's will of justice and peace for all humankind, we have no business either complaining or getting in the way. If, as I suspect, you are talking about the Church of England, rather than the Church as such, then they too should welcome pressure from government to put their ethical house in order, particularly as regards continued discrimination on ground of gender (still no women bishops), let alone sexuality.
The Rev DAVID J M COLEMAN