A commenter who identifies himself as a Riverside atheist who supported keeping the cross commented on the situation over at the Friendly Atheist blog:
"Mt. Rubidoux was originally owned by Riverside Pioneer Frank Miller, he built the cross as a monument to Father Serra who was a very important person in early California history. President Taft commemorated the Serra Monument in 1909. Frank Miller and the Miller family owned Mt. Rubidoux until the 1955 when he gifted it to the City of Riverside as a park with a 30 year condition that the Cross remain in place...
"As an atheist I see the Serra Monument in a proper historical context and can observe that this was important to many of the early settlers of my community even if I no longer believe in the religion which they did. There are many other churches and religious icons on public property which are maintained to to their historical importance."
He likens tearing down the cross to the radical Muslim removal of statues and monuments (which I discussed here). It's an interesting point. There are crosses and religious monuments with sufficient historical gravity that they should probably remain on public land (I'll again throw out the Cape Henry cross in Virginia Beach as an example). The Riverside cross seems particularly difficult to me because it seems to loom over the town in a really dominating way (the Cape Henry cross is actually on a military installation, and you have to show ID and registration just to be allowed to see it).
I would not like to see atheists become so radical that we advocate tearing down genuine historical artifacts. The problem is that the "history" argument gets pulled out too readily by those with Christian privilege-- for example, all those Ten Commandments monuments left over from the 'fifties are supposedly "historical" and thus sacrosanct. It can be quite difficult to differentiate between a monument with genuine historical significance, and one that is not really of any historical value or interest.