Politics in Oz
The whole idea of politics in Oz has been around for a while.
Baum himself was asked whether his stories had hidden meanings, but he always replied that they were written to "please children".
says the Wikipedia article, and the book it cites, Oz in Perspective: Magic and Myth in the L. Frank Baum Books, agrees, but then goes on to say
However, in his statement about writing "only to please children," Baum undoubtedly is distorting the truth.
The same book says
That Baum had at least a mild interest in politics and political movements and that he worked his interest into his Oz books is well documented.
The note after this sentence cites
- Littlefield; Erisman, "L. Frank Baum and the Progressive Dilemma"
- Cook; Geer and Rochon; and Koupal, "Wonderful Wizard of the West"
- "The Politics of Oz: A Symposium" that includes Gessel; Koupal, "Add a Pinch", and Erisman, "L. Frank Baum and the American Literary Tradition"
Ozma of Oz political background
Until Ozma of Oz comes into the picture, it's interesting to note that the political landscape (if I may use such a term referring to a children's storybook) of Oz is rather fragmented. We go from the Wizard of Oz to the Scarecrow with a lot of tumult, and inbetween there are witches, and distant lands still in Oz that are really under nobody's control. The politics start with the second Oz book, The Marvelous Land of Oz (quote from Wikipedia article):
They learn from Glinda that after the fall of Oz's mortal king Pastoria decades ago, a long lost princess named Ozma was hidden away in secrecy when the Wizard of Oz took the throne. She also informs them that Ozma is the rightful ruler of the Emerald City and all of Oz in general, not the Scarecrow (who did not really want the job anyway). [...]
The restored Ozma is established on the throne after defeating Jinjur and her army.
So, placing the proper ruler on the throne, defeating a rebel army, and making Ozma look good (Tip has been the hero for most of the book when this twist comes into play).
When Ozma of Oz comes in, she becomes the ruler of Oz. From there, most of the Oz stories are about keeping her in power or extending it - a decidedly political turn. For example (quotes in this section taken from this Wikipedia article:
In Ozma of Oz
they must save Ev's royal family from the evil Nome King. With Princess Ozma's help, they finally return to Oz.
They defeat the Nome King to preserve Ozma's kingdom and also to replace the Princess Langwidere with more capable rulers in Ev.
In The Emerald City of Oz
the Nome King is tunneling beneath the desert to invade Oz.
They must preserve Ozma's kingdom.
In The Patchwork Girl of Oz
A Munchkin boy named Ojo must find a cure to free his Uncle Nunkie from a magical spell that has turned him into a statue. With the help of Scraps, an anthropomorphic patchwork doll, Ojo journeys through Oz to save his uncle.
What this doesn't mention is that a major plot point is the illegality of using one of the ingredients Ojo must collect, so much of the story ends up centering on laws, mercy, and justice. Ozma here again features significantly.
Tik-Tok of Oz:
the two try to rescue the Shaggy Man's brother from the Nome King.
Again, defeating the Nome King and preserving Ozma's kingdom is a significant plot point.
The Scarecrow of Oz:
Cap'n Bill and Trot journey to Oz and, with the help of the Scarecrow, the former ruler of Oz, overthrow the villainous King Krewl of Jinxland.
Here, again, defeating an enemy and extending/preserving Oz territory are a feature.
The Lost Princess of Oz:
When Princess Ozma mysteriously disappears, four search parties are sent out, one for each of Oz's four countries. Most of the book covers Dorothy and the Wizard's efforts to find her.
Finding Ozma and therefore preserving her rule is the main plot point, and defeating evil in Oz.
The Magic of Oz:
Ruggedo, former Nome King, tries to conquer Oz again
Again, preserving Ozma's rule and defeating enemies.
Glinda of Oz:
Dorothy, Ozma and Glinda try to stop a war in the Gillikin Country.
Stopping a war and preserving Ozma's rule again!
To summarize from all of this, it's pretty clear that Baum's books focused on the stability, unity, and endurability of government, even if it was fictional. Returning again to Oz in Perspective, it says
[Baum's books] treat important aspects of politics. They can easily be seen as embodying Baum's reaction to the corruption, instability, and lack of unity that characterized America during large portions of his life. And since the solutions to the problems of government in Oz involve magic, it is easy to theorize that Baum felt that in the real world of his day, many political problems were insoluble.
This, and the earlier citations referring to scholar's analysis of the politics of Oz points to political allegory having at least some play in the Oz tales. (Interestingly enough, Baum wrote for the Aberdeen Times earlier in his life, and wrote several politically focused articles and editorials.)
Your actual question
Now, all of this being covered, to treat your actual question.
Princess Langwidere is cited as vain and too busy admiring herself to actually do administrative tasks, and that she doesn't really enjoy affairs of state. (See the Wikipedia article if you wish; this can also be found here in the Google books copy.) Since she doesn't want to be bothered, she specifically tricks people with the sign you mention in your question.
Baum was annoyed by instability, and this is much the situation here - the only ruler of Ev is a vain, disinterested Princess, who doesn't keep things in order or do much of anything. If that's not the definition of unstable, I don't know what is.
Baum then uses Princess Langwidere as a reason to go on a dangerous quest to replace her with a more capable ruler. The whole situation here is political, and it is almost certainly one of the general political references the aforementioned scholars have noticed throughout Baum's work. However, whether this specific joke is about the right versus the left wing in politics is difficult to tell.
Interestingly enough, Baum himself was sympathetic to the Populists and voted for the Democrats (source):
Baum was sympathetic to the Populist movement, supported William Jennings Bryan in the election of 1896, and, though not an activist, consistently voted for Democratic candidates. (In 1896, the Populists joined the Democrats in backing Bryan’s bid for the presidency.)
The Populists ended up merging with the Democrats soon after they supported Bryan, which fits with your thoughts of right wings portrayed as left wings, except that the Populists were also left wing, generally speaking. Interestingly, though, the Populists were mostly farmers, who are normally right wing, but were angry with
what they perceived to be the interests of the Eastern establishment and banking elite
(Quote from Khan Academy.) They were then a sort of inbetween group - some left-wing and right-wing - and when the Populist party merged with the Democratic party, it isn't inconceivable to think of it as becoming slightly more right wing.
Baum's books were actually decently influenced by the politics of his time, so it's not impossible that the left/right wing joke in Ozma of Oz is also political, referencing the Populists merging with Democrats, and I think it is somewhat likely given the relative position of each party and the many-times espoused parallels between Oz's stance on some issues and the Populists' stance on those issues.