But anarchists were a distinct and active political force in Spain during (and before) the Spanish Civil War. I suspect the page is talking about those anarchists. The Catholic Church was on Franco's side during the Civil War so a church wouldn't have been an unreasonable target for left-wing anarchists, though I have no idea if the claim is true.
Yes, Anarchist were very much a specific thing in that context, not as its used today.
I don't know how true to history the movie is, but if close, then "La Lengua de las mariposas" is a good example of basically anyone possibly being accused of being an anarchist at that time, if they were againt the Franco regime.