Using random-phase approximation spin-fluctuation theory, we study the influence of the hybridization between iron $d$-orbitals and pnictide $p$-orbitals on the superconducting pairing state in iron-based superconductors. The calculations are performed for a 16-orbital Hubbard-Hund tight-binding model of BaFe$_2$As$_2$ that includes the As-$p$ orbital degrees of freedom in addition to the Fe-$d$ orbitals and compared to calculations for a 10-orbital Fe-$d$ only model. In both models we find a leading $s^pm$ pairing state and a subleading $d_ {x^2-y^2}$-wave state in the parent compound. Upon doping, we find that the $s^pm$ state remains the leading state in the 16-orbital model up to a doping level of 0.475 electrons per unit cell, at which the hole Fermi surface pockets at the zone center start to disappear. This is in contrast to the 10-orbital model, where the $d$-wave state becomes the leading state at a doping of less than 0.2 electrons. This improved stability of $s^pm$ pairing is found to arise from a decrease of $d_{xy}$ orbital weight on the electron pockets due to hybridization with the As-$p$ orbitals and the resulting reduction of near $(pi,pi)$ spin-fluctuation scattering which favors the competing $d$-wave state. These results show that the orbital dependent hybridization of Fermi surface Bloch states with the usually neglected $p$-orbital states is an important ingredient in an improved itinerant pairing theory.
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