As a point of clarification, Byrne's Superman was not a vigilante. He was deputized to make arrests and enforce law, and was authorized by President Reagan to act on behalf of the United States. In fact, he comes into conflict with Batman and Gangbuster right away because he makes it clear he does not tolerate vigilante methods.
Whether you agree or disagree with Superman executing the Kryptonians generally depends on three things - whether he had the authority to execute them, whether there was enough evidence to find them guilty and sentence them in absence of a judge & jury, and whether they posed a threat to prime Earth.