Stiles's reactions are in part related to deleted dialog from the episode (see this article on Orion Press for the full details
INSERT - SHIP'S VIEWING SCREEN
The attacking vessel can now be seen definitely to be some modified version of a starship saucer main section...........
You see it, Enterprise?! Starship
design. Warn Earth...
... espionage, stolen our designs... traitors...
Then later, before the reveal of the Romulans, Kirk and Stiles' exchange in the script is:
... and in a vessel remarkably similar
to ours. The Outpost Commander
mentioned "espionage." Add to that
the fact it was a sneak attack...
Are you questioning my orders,
Negative, sir. I'm pointing out that
we don't even know what the
Romulans look like, maybe just like
us. We could have Romulans aboard
our own ship.
So, by the time they SEE the Romulans, Stiles has already had suspicions of Romulan spies, and lo and behold, Spock looks just like one.
Now those line would've helped things along a bit, feeding Stiles' paranoia.
And yes, I've read about unreconstructed Southerners. (There's a really great book called "The Walls of Jericho" about how difficult southerners made passing civil rights legislation in the Senate). I would point out that while the Civil War ended in 1865, Reconstruction existed for nearly a generation after this. (Hence the term "unreconstructed")
While it temporarily brought great political and economic advancements to many African Americans in the south (amazingly, the first ever African American US senator was from Mississippi in 1870), it was loathed by southern whites.
Most of the white southerners in positions of authority who resisted civil rights in the mid 20th century (which was about 99% of them) would have either been born during or shortly after Reconstruction, or been the children of those that were.
And BTW, I've always been puzzled why some southerners found the term "war between the states" more palatable than "civil war", apart from the fact that there's nothing "civil" about any war. (Don't even get me started on the calling it the "war of northern agression").