The opacity, pressure and temperature all vary as a function of position in a star. For a spherically symmetric star you can assume they vary only as a function of the radial coordinate $r$.
The reason that luminosity and mass are written as $L(r)$ and $m(r)$ is to remind us that these do vary with radial coordinate and avoid confusion with the luminosity and mass of the entire star, which are meaningful and observable quantities. $L_* = L(R)$ and $M_* = m(R)$ respectively, where $R$ is the radius of the star.