Should human rights always outweigh religious rights?
Neither, because the idea of "rights" is flawed. It is bad philosophy, which in turn produces various problems and conflicts. An idea of "right" puts responsibility on others. "I have the right and now you have to do something." The order or any morality for that matter falls apart as consequence. In contemporary sense a right is whatever government says it is right. It is just as Christopher Ferrara eloquently puts it: "Modern society is atomized individual powerless against all powerful state." and "God gave us ten commandments not rights!" I strongly recommend you to watch all his talks about Christian social order, morality and law, the kingship of Jesus Christ and liberal secular state (on Youtube here).
Modern state claims for itself an absolute authority in regards to all things concerning social order (including morality). In consequence it leads to absurd praxis that morality is defined by democratic vote (by majority public opinion). This is utterly false and dangerous position to hold. For example if majority people would desire to exterminate Jews it would be permissible and moral since morality is viewed by prism of what is legal (or a legal right). In this construct of self-determined voted on national morality is everything subject to trends and whims of the society. In the framework of Lockean secularism based on religious indifferentism any moral argument holds no value as everything must be tolerated. That is why in The Big Questions any effort to justify upholding morality on grounds of secularism and pluralism is doomed to fail. Any religion or individual believer in conflict with this system is going to be struck down (that is the persecution they clumsily talk about in the video).
The idea of religious rights or freedom of religion is somewhat coming from the state is ridiculous. I have never seen any religious authority to check bill of rights, consult lawyer whether some religious truth is not in conflict with the law of the land. It is mentality of reversed order, where secular (agnostic) state is superior to religion (religious authority). This is one of the errors condemned by Bl. Pius IX.
What is necessary is to shift debate on the other side of the coin. It is necessary to abandon the right talk. This means I have a duty (a moral obligation) and you have a duty. The first duty in Christian framework is to believe in God. State has duty to protect the true religion of Christ the Catholic Church. If society orders itself around duties required by the God and the true religion of Catholic Church (not those schismatic and heretics like Church of England, countless protestants sects, etc.), no moral man would miss so called rights for a second. So I can say:
"I do not recognize any limitations established by law upon proclaiming or upholding truths of the Catholic faith, the only true religion, because my duties to the One true God supersede my duties to the state or any individual man."
"Moreover It is necessary to refuse safety blanket of religious freedom and other secular rights, which in practice serve as unspoken social contract to permit various immoralities violating natural or divine law in exchange for silence. Following example of St. Francis of Assisi, who returned everything to his father including clothes, it is time to return all secular rights to the state including religious rights, freedom of speech, etc. and embrace Christ without comforting chains of lukewarmness forged by godless ideologies."
