How does the opera Carmen tie to typical operatic plots and themes?

In order to answer this, we first have to define which sub-category of opera we're describing Carmen as being typical of. By 1875, when Carmen premiered, there was a vast diversity among operatic plots and the musical forms composers used in their treatments of the literary material with which they worked. Carmen, though it was premiered at the Opéra-Comique in Paris, is a serious drama, a tragedy. The ending, in which Carmen is murdered by her lover, stunned its first audiences and still has the dramatic force to shock people who are not already familiar with the plot when they see it on the stage today.
On one level Carmen can be said to be typical of operatic works on love. Often an opera librettist, in adapting a play or novel, would take a complex story with multiple themes and reduce it to a relatively simple love story. In French opera, this is the case not only with Bizet's Carmen, in which Prosper Merimée's story is streamlined, but in adaptations of Goethe and Shakespeare by Charles Gounod and Ambroise Thomas as well. What is unusual in Bizet's case is the astonishing richness and complexity of his music in comparison with that of his French contemporaries, for the most part. But this fact about the music leads us to another point about Carmen that links it to other outstanding operas in the repertoire.
If one were to read the libretto of Carmen, without having heard the music or having any knowledge of it, one would probably not think there was anything outstanding about it artistically. The characters might seem to be stereotypes. Don José is the model of a man rather unintelligently smitten with the shallow, insensitive woman Carmen is—another stereotype, and definitely a sexist or even misogynistic one. But Bizet's music transforms the characters, and the story overall, into a work of such depth and beauty that intellectuals, to say nothing of the opera-going public in general, have been overwhelmed by it. Though some of the greatest operas have been based on the works of the greatest authors—Hugo and Shakespeare for Verdi's works, for example—it has been more frequent for undistinguished material to be made, through the power of music, into incomparably great operas. This is true of Mozart's Cosi fan tutte and The Magic Flute, as well as most of Verdi's operas (the ones based on Hugo, Shakespeare, and Dumas are the minority). Bizet's masterpiece fits into our general observation. It has been considered by many to be the greatest opera ever written, though the story on which it is based is, by itself, relatively undistinguished and abounding in stereotypes.