There is an atheist argument, "Religious people are only religious because they want to control other people or are controlled by them. Religion is a system of authoritarian control."
There is a religious argument, "Atheists are only atheists because they want to rebel against God. Atheism is an act of rebellion."
Are these extensionally equivalent?
Are there other common arguments from opposed viewpoints that pair up like this?
I don't think its accurate to describe them as an opposite pair, more that they both share the same premise (people consider control important/motivating) and derive different conclusions.
You could generate an arbitrarily large number of other predictions from that premise, e.g. Greens support geen policies because they want to control people, blues support blue policies because they don't like the idea of being controlled.