From the lack of responses it seems that not many here are using surge protectors. Maybe not really an issue to be concerned about? Next time I plug into shore power I'll try one of the power strips I have laying around. The only real draw would be the frig and furnace.
If plugging in a cheap generator or inverter I think I'd worry more about the waveform of that AC than any surges. I doubt most of them have enough guts to produce a serious surge, but wild waveforms, square or whatever, is the mark of the cheap stuff. Your batteries won't care, (though your charge controller might) but the delicate electronics in everything these days might work but very inefficient, or not work but not be be damaged, or just plain die (immediately or later). It's a risk.
The clean sine wave stuff costs more, but that's what I try to stick with.
Strange surges are not limited to your AC. When motor vehicles start up the 12 volt can have some damaging spikes and such. Generally it cleans up once the engine is running and battery being recharged. Between the truck and my house battery camper system I have a voltage sensing relay setup. It's primarily there to keep from draining the start battery when stopped, but the small delay until it joins the batteries for charging is enough to provide a lot of safety for the electronics.
The available designs for multi battery, multi charging systems has been evolving rapidly. I put a current state of the art dual battery system into the small outboard boat we got for photography last year. Both batteries maintained by either plugging into 110 or the outboard. What I put in works fine, but is also obsolete with better stuff this year. The Eagle is going to be more complicated than that, limited primarily by how complex is necessary rather than how much is possible.