As far as I know, only the Roman Catholic Church has made the issue of "conscience" actual doctrine in their theology. This does not mean that other religions have not included it or touched on it in their theology (or that I have likely missed study of a religious group that has done so), but Catholicism has raised points dogmatically demanded upon members as part of their convictions and practice since Vatican II.
The Catechism of the Catholic Church (the official compendium of Catholic doctrine as it now stands since Vatican II) states the following about conscience:
Man has the right to act in conscience and in freedom so as personally to make moral decisions. "He must not be forced to act contrary to his conscience. Nor must he be prevented from acting according to his conscience, especially in religious matters."--CCC 1782.
This now exists in Catholicism because that religion recognized grave and "sinful" errors on behalf of many of its members in various moments in the Church's own history where because of failing to recognize the freedom of conscience of other humans the Church itself, according to its own admission, committed grave offenses against God.
One of the most famous cases in which the Catholic Church admits it violated the principle of religious freedom for its own members is the case of St. Joan of Arc. In attempting to force Jeanne d'Arc to recant her actions and statements regarding personal revelations from heaven, the Church used extreme force on another human in an attempt to stop her communication with what Jeanne claimed were angels and saints offering her direction from God and attempted to dictate how Jeanne could or could not dress in response. In other words, as poetically expressed in the stage version written centuries later by George Bernard Shaw, the Church was 'punishing her for talking to God.' As history shows this young woman was burned at the stake for stating should would not violate her conscience in how she worshiped or the type of clothing she wished to wear.
The Church would later exonerate her of all charges, and after 500 years of examination into her case quite embarrassingly canonized her as a saint.
Her case is not the only instance the Church worked against itself. You would think a religion like Catholicism would want people to believe in earthly visions and miracles, but it likewise persecuted another French maiden, Bernadette Soubirous who received visions of the Virgin Mary, and several centuries again attempted to silence the events surrounding alleged appearances of the Virgin Mary to three children near Fatima, Portugal. Both situations would have the Church acquiesce to their validity, with St. Bernadette discovering the famed fountain at Lourdes, France and the apparitions in Fatima ending in the only alleged modern-day "miracle" witnessed by a large crowd of people.*
The Church has hoped to have learned its lesson, but as years have passed since Vatican II various popes have had to issue formal apologies for the violation of its own principles, not only to the Jews, but to Protestants, such as the recent papal apology from Pope Francis for the Church's persecution of the Waldensians. Many Catholics believe that the Holy See will eventually change its views regarding homosexuality, and thus predict that its current stand will again find the Church apologizing for being on the wrong side of history once more.
The cases involving St. Joan of Arc and the others following have involved testimony within the Church that religious freedom had been violated, but I have not seen this taken to an actual secular court. I also am not aware of the issue of freedom of conscience being considered a human right by any other religion in the same dogmatic fashion, definitely not in Watchtower theology.
*-The mention of the "miracles" in this post are not to be viewed as a personal belief in these events, in any formal religion, or inviting posts to disprove the events. The reality or lack thereof of the events being mentioned is not the point. The focus is that the Catholic Church, like the Jews who rejected Christ, often rejected its own so-called "prophets" and their "prophecies," even to the point of murdering the "messengers from God" in order to silence the alleged "messages from Heaven" and even, in the case of Lourdes and Fatima, to prevent crowds from witnessing "miracles" through force. The argument is not that these things are real or not, but that the Catholic Church understands very well that power can be so intoxicating that it can, will, and has caused faithful Catholics to "bite off their own foot in spite of themselves." Realizing the paradox caused by such ironic actions, the Church has made it a doctrine that any attempt to prevent a person from acting in accordance with their own conscience in matters religious, even in the rejection thereof, is a grave error. This still has not prevented the Church from repeating its mistakes in history, as it seems that all religions have a lust for silencing Heaven through bloodshed if necessary.