General Assembly
He was ordained an Elder on appointment as professor of Greek and ever since then had been returned as representative of the university, or of the presbytery, to the General Assembly of the Church of Scotland at its yearly meetings. When he became a minister and progressed as an academic, his influence in the assembly grew. His speaking skills were considerable and had always been an excellent networker, noted for his conciliatory approach. He had closely studied the history, law and procedures of the General Assembly, so he was a formidable operator. Principal William Robertson was the leader of the so-called Moderates. These saw themselves as enlightened Calvinists and Presbyterians who were prepared to compromise with the Government in many matters - in particular, over the issue of Patronage - but not on the spiritual independence of the Church. George Hill was one of this party, and took over the leadership of it when Robertson died. He was a very sincere Calvinist and a proud Presbyterian, but did not take a gloomy view of the former, and accepted that landowners (the Heritors) who paid a Minister's salary had some rights in their appointment. But he was fiercely protective of the independence of the Church. In 1782, when the Lord Advocate seemed to threaten him for his views that the usual address to the Crown was too political, he said The Church of Scotland is independent of any party and any Ministry; he cared not for the threats of the learned gentleman, and he might tell his friends in power that he had said so.
During the French Revolutionary Wars, he vigorously opposed a plan to get Parish Ministers to urge support for a voluntary levy, as compromising the political independence of the Church and unseemly for a pacific profession. He was much opposed and vituperated but he stood firm. He would willingly contribute himself, but would "strip the gown from his back rather than obey an order to promote it from the pulpit". This was extraordinary for a man renowned as a British patriot - he expressed the hope "that this island will continue, to the latest ages, the fair seat of regulated freedom, of rational religion and public virtue"- and a Moderate (inveterate compromisers with the Government according to their enemies). The plan was dropped. But he was usually conciliatory as well as effective. In the year he was Moderator (1789) there were unusually violent squabbles over the appointment of a new Clerk to the General Assembly. At one point, Dr Hill had to suspend the Assembly. However, after the wrangles, the Assembly voted That the thanks of the House should be given to the Moderator for his most impartial, dignified, and able conduct in a very delicate and uncommon situation during all the preceding diets of this venerable Assembly. He continued to attend the Assembly until 1807 when he was too infirm to travel to Edinburgh. For instance, he argued strongly against Professor John Leslie who had written an Essay on Heat, which was thought to echo too closely some sceptical philosophic views of David Hume, and were therefore "destructive of religion". Principal Hill agreed when the Assembly had been asked to censure him. The public crowded in to hear the obscure debates, but in the end, the Assembly dismissed the complaints.