Have Batman movies always had a political influence upon them?

The character of Batman is older than you may think... unless you have already begun to research him. For example, his first comic appearance in 1939 had him killing and maiming criminals. That's quite a different Batman from the one he developed into over time. In that first year it was explained that Batman became the superhero he was to avenge the death of his parents.

Now, step back a moment. The comics of 1939 were not nearly as in-depth and detailed as they are today. Batman was the protector of Gotham City, because as far as that specific comic strip was concerned, Gotham City was the entire world. I'm not saying that it spanned the globe in that comic... just that it was essentially pulp fiction about a dark crime fighter protecting a city. The reader didn't need much more than that to enjoy the story.

After a storyline in 1940 "in which Batman shoots some monstrous giants to death" the editor of the comic decides that Batman is no longer allowed to kill or use a gun. This was also the year Robin was added, and the character was softened a bit.

In the years following World War II, DC Comics "adopted a postwar editorial direction that increasingly de-emphasized social commentary in favor of lighthearted juvenile fantasy." The impact of this editorial approach was evident in Batman comics of the postwar period; removed from the "bleak and menacing world" of the strips of the early 1940s, Batman was instead portrayed as a respectable citizen and paternal figure that inhabited a "bright and colorful" environment.

From Wikipedia

So, the motives that spurred Batman on weren't always necessarily political... but you do have to remember here that we are talking about a crime fighter. He was created to fight crime as a vigilante, and do what the police were either unable or unwilling to do, or incapable of doing. This does mean that sometimes there would appear to be some kind of political tie to his actions. One might be prompted to ask if the police were really that incompetent if Batman is always the one chasing down the bank robbers, but the comic series was about Batman fighting crime... not about the police doing their jobs.

Now... you step Batman out of his original comic beginnings, and you have to see him instead as the reinvention of the people who are presenting him. The Batman of the original comic series is a different Batman from the TV series out of the mid 60's. This Batman is a different Batman from the Dark Knight introduced in the mid 80's, who in turn was a different Batman we saw in the first movies (starring Val Kilmer, George Clooney, and Michael Keaton). The Batman portrayed by Christian Bale was again a reinvention of the character.

The idea of Batman in Gotham City, isolated from the rest of the world (because it didn't exist) couldn't stand the light of day (or the moon) by the time Christian Bale stepped into the role. The Batman we are introduced to is a global Batman, and Gotham City is more like a real city than a comic-book one. The City as a character even transforms over time, over the series of these movies. Take for example the multi-level suspended tramway that is so significant in the "death" of Ra's al Ghul. It was one of the crowning jewels of what Bruce Wayne's father had given to the city, and is completely gone by the second film in the DK series. Gotham City has all but completely transformed into New York in The Dark Knight. This transformation for a major character (for Gotham City is indeed a character in the Batman stories) from an element of fantasy to one of super-reality is indicative of how the stories being told by Christopher Nolan are to revolve less around fantasy, and more around reality... something that the viewer can relate to easier.

It is important to remember, so much so that I must repeat it, that above everything... Batman is an example of a normal man, pushed to an extreme, who takes the law into his own hands in such a way that viewers can get behind him... rather than condemn him for putting himself above the law. In order to be able to see him as a hero, the situations we see Batman in mustn't be ambiguous. It must appear as if the police are inept or corrupt, or that the criminal is too smart or powerful for the police to stop. As the stories that Batman is woven into become more realistic, the reasons that drive his actions will indeed appear to become more political... simply because characters like Mr. Freeze and the Penguin don't fit into that realistic picture. If he can't fight some over-the-top villain, he must fight some "evil" that the audience can more easily recognize. Today, that is usually related to something political.

Batman stories are almost always set in Gotham City, and a Gotham is almost always depicted with varying levels of governmental corruption of some degree. Batman's hunting grounds is what TV Tropes calls a Vice City. So given this setting the city's politics is definitely a common story element: Batman having to deal with corrupt officials, criminals trying to shape legislation ... etc. But I would not say that it is the most prevalent story element in Batman stories.

I would say that Batman is not about politics directly. It is however very much about law, order, and justice. Because of these themes, it can very easily be drawn into politics.

Individuals running for Mayor or District Attorney often have to take a though stance on crime. This can both ally them with the Batman or put them at odds with him as they try to crack down on this street vigilante. Bringing in the Batman would be a great media-flashy (and to a would-be mayor, easily done: "He's just ONE MAN") way to show your hard anti-crime work (without actually confronting the problems themselves). Also, the presence and need for the Batman makes their own though-crime efforts look bad.

Beyond that, Batman is a constant thorn in the side of Gotham's organized crime, who often have a ties into politics though corrupt politicians and bribery. This can also easily cause a more politically-themed story line.

All in all, due to the tight coupling of crime and politics in a variety of ways, Batman, while not directly about politics, finds it's way there often. You can see examples of this sort of thing in other series too, a prime example being The Wire.