Well, it’s certainly not a case of brutal government persecuting unresisting Christians as in ancient Rome.
While the government was certainly brutal enough, the Catholics resisted quite effectively, to the point that estimates have considerably more casualties on the federal side than on that of the rebels.
You can call that religious persecution if you like, but it looks a lot more like a civil war to me.
To answer your question directly, there are degrees of moral equivalence. Seldom in human affairs is one side utterly evil and the other totally good. So most of the time either accepting full moral equivalence or rejecting it completely is inappropriate.
The question is (usually) not one of whether moral equivalence exists, it is one of how much in a particular case.
“Well, it’s certainly not a case of brutal government persecuting unresisting Christians as in ancient Rome.”
It started that way, as it did in Spain a few years later. In Spain the army revolted against the elected government when it took no action to protect the Church or even basic property rights from the Bolshevik mobs; the Communist government literally outlawed Mass (and killed twelve or thirteen bishops, on top of thousands of priests and dozens of nuns). As in Mexico, many of those religious also proclaimed “Viva Cristo Rey!” as they were martyred; it became the battle cry of the Carlists on the Nationalist side.
The current (Leftist) government of Spain has erased that history; thankfully the Vatican has been canonizing the martyrs of the war in Spain (and some from Mexico as well) so that nobody can deny the events of the first half of the 20th century. The Left is still as focused as it was then, and has lulled people into complacency as they divert attention to nonsense while they keep Marx’s dream alive.