"There is also a saying that goes "Don't kill chilangos: if you do, ten more will show up for the funeral and five are bound to move here".
The bumper stickers are a radical expressions of rather generalized unease with people from Mexico City (words like dislike or mistrust are too strong). The worst it usually comes to are cars with Mexico City plates being scratched in places like Sinaloa or Jalisco. Occasionally people get shot, as would happen in many US States.
The roots of this unease are many and debatable. First of all, people resent being ordered around by remote control, which is the way Mexico was ruled since the 1830s, despite being a "federation of free and sovereign states" (my history on the subject is fuzzy). Central control was exacerbated under the Porfiriato (1876-1910) (Don Porfirio had a policy of appointing people he trusted as Governors in the more distant states, and keeping his enemies close by), and by the PRI regimes. The reason the PRI (or the PRN) came about was, precisely, to unify rebel factions around the country in a single, centralized political movement, hence its lack of a clear-cut ideology. The independence of Texas was also a reflection of the resentment to an excessively centralized government.
Like New York in the US, Mexico City is a larger, more impersonal place than any other in the country. This brings greater tolerance as well as greater uncertainty and insecurity. Few of these traits are appreciated in less urban (read, more traditional) environments.
On top of that, there are regional chauvinisms (on all sides). Chilangos tend to regard Provincianos as... well, provincial, and are perceived to be arrogant as well as ignorant and disrespectful of local customs. Incidentally, this problem of perceptions is beginnng to worsen for Regios (from Monterrey), and Tapatíos [or derisively, Jalisquillos] (from Guadalajara).
Another, more recent, reason for dislike is that since the 1985 earthquake, thousands of Chilangos have moved out of Mexico City to places like Cuernavaca, Querétaro and Guadalajara, driven by the desire for simpler lifestyles. In many cases they have formed virtual colonies (it is, after all, difficult to be assimilated into local cultural and business circles) with their own schools, church congregations, neighborhoods, etc., that are relatively separate from the local populations.
It is ironical that there are very few true-blue, native Chilangos. Most of our parents (or grand-parents at the outside) came to Mexico City from other parts of the country (Campeche, Puebla, San Luis Potosí and the US in my case).