With the election coming up in November, I'm quite sure I can come up with plenty of designs for both sides of the political aisle.
I really think that the GOP store and the Democratic store should be separate from each other. If I open two more stores, how separate will they be? Can I "hide" the fact that I'm selling to both sides?

Since the stores will be separate (you'll see a list of all of your stores in your account), as long as they don't have the same names, you don't add links to guide people to your other store or tell them in the forums, it shouldn't be a problem.

I have two stores and I know people here with dozens of stores. One seller has over twenty stores.

With my two stores, I have different usernames, too, so if I didn't tell anyone that I'm also the owner of dreamNwish Wedding Designs (aka DNW Wedding Designs), they wouldn't know any better. They'd just think I have dreamNwish Photo Art. I sometimes log into the forum under DNW Wedding Designs, so if you don't want people to make the connection, be sure you're logged in with the account you want to discuss topics for that particular store.

I know of one person with a politcal store. They said they never sign in under that account as not to accidentally get confused and post something that gives them away.