A question

John Adams, Robespierre, Burke, Richard Price, and Pius VI all agreed there was something wrong with the public atheism of the philosophes that were behind the French Revolution. Adams and Richard Price were friends. Richard Price was the leader of the radical dissenters in England, who were very supportive of the French Revolution. Burke was a Whig, who eventually became known as a leading "Conservative." Pius VI was the Pope, of course, who eventually was imprisoned by the revolutionaries themselves, and he died in exile.

From the standpoint of philosophical worldview, Adams, Robespierre, Price, and Burke all shared common assumptions about human nature and religion. Why, then, would they end up being percieved as "opposites" in modern politics?