There is no proof of an association of the naming of schools with the Civil Rights Movement. Jacksonville already had schools named after Confederate Generals. It would be far easier to say that the names were chosen to follow the trend started in the late 20's. You have no grounds to re-name this school other than a disputed association with a long vanquished (idiotic) organization. If the activist are really only concerned with this association then by all means choose another Confederate hero to name the school...at least then they can keep their Mascot. That would show that this is not just a racial attack on southern heritage.
So for you this is all about preserving a certain part of "Southern" heritage? That's cool but for a lot of people out there, that's not what this is about. That's certainly not my perspective.
There's also no trend starting in the 20s that carries through to the naming of Forrest. For example, you've got schools like Terry Parker, Ribault, Paxon, Fletcher, Englewood, Douglas Anderson, etc. sprinkled in there between the 1920s and 1959.
Last, this isn't an act of war, it's a name change. The only grounds needed to change the name of the school or anything else locally is a majority of the public demanding it. As I said earlier, I truly feel it will eventually change because as time goes on, the city will continue to get more diverse and the community's desires will morph to that of it's demographics. To that effect, it is what it is.