A (usually) derisive reference to Ann Arbor, used to equate the liberal politics of the town with the communist government of the People's Republic of China.

Ann Arbor has taken a number of actions over the years that cause people to view it as left of center, including instituting a bottle bill that pre-dated the State of Michigan's, mandating a living wage for employees of the City or the City's contractors, and creation of the Greenbelt. Sometimes this tendency has verged into the surreal, such as a proposed animal rights ordinance in the early 2000s that saw City Council debating what constituted human companionship for goldfish.

Sister cities in this regard

Several other cities across the USA get this naming. E.g:

Sources

Have a lovely weekend, Wonketteers. I’m spending my weekend in Real America, the Appalachian Mountains of North Carolina. Actually, I’m headed to the People’s Republic of Asheville, where the lesbians grow thick and wild and white men with dreadlocks roam under the full moon eclipse, searching for magic mushrooms and holy crystals and a nice place to smoke the dank, brah.

People usually think that Iowans are overstating things when they speak of the seat of the University of Iowa as "the People's Republic of Iowa City." But every once in an while, something happens that demonstrates just how extreme and distorted things get out there.

A prefix, referring to a liberal community in a derogatory manner. Generally applied by conservatives (i.e., Rush Limbaugh), but occasionally one of the more fledgling communities will subtly apply the term to itself, in an effort to seem cool and oppressed in liberal circles.