Greco-Roman philosophers declared that animals could not partake of human justice because they could not partake of human reason. In opposition to this, Plutarch asked if animals could be granted kindness if not justice. I forget the exact spot in Plutarch's works, but it is there somewhere. So among the intellectual elite there was one lone voice ...?
Spiritually, there is nothing per se in Roman religion that lends itself to environmentalism or 'animal rights.' Animal sacrifice was the cornerstone of public ritual. Some religious cults objected but these were few. Robert Turcan claims that before Romans cleared a glade of woods, they first made a sacrifice to propitiate any spirits that lived there; but once sacrifice was made, the land would be cleared for human development...
The Roman state crucified two dogs every year in memory of the guard dogs that supposedly did not bark to warn of approaching Gauls when the Capitol was under siege. Romans soldiers made a point to kill everything living when they stormed a city, including dogs on the street.
As to the animals slaughtered in the Ampitheatre, they became tasty treats for the hungry plebians. Can't imagine the masses were therefore interested in the preservation of a few elephants (what does elephant taste like? Chicken?).
Roman intelligentsia mocked the animal fetish inherent in Egyptian religion.
The picture I get is there is very little in the Roman tradition that lends itself to environmentalism.