The great thing about the Eastern Gray/Western Gray ID issue is that they have VERY little crossover habitat. The only area I'm aware of that you have to be keenly aware of the ID is in the south Puget Sound area.
Also, the California Ground Squirrel and Eastern Fox Squirrel are also not protected, but are rather challenging to find. I've gone after the California Ground variety and have yet to actually see one.
I do target them. Find an area you know they are and just wait for one to stop moving long enough to get a shot. I use a .177 air rifle with a varmint scope. I got 2 of them last year. None this year. The problem is more around finding them in a spot you can have a firearm or air rifle out and use it where they live. I've heard of folks trapping them in their yards or baiting them and you're free to do both, I just don't because I'm less interested in getting them that way.
With the number of Douglas Squirrels I see every year out in the woods, it's truly shocking that they are protected. I see hundreds if not thousands, maybe tens of thousands every year in the woods. I probably See one at all times. 99.99999% of the movement I see in the woods are the damn Douglas Squirrels. They are awfully small though, so maybe the harvest-able meat is just too little to justify allowing the public to hunt them.