Most quantum key distribution (QKD) schemes exploiting orbital angular momentum (OAM) carrying optical beams are based on conventional set-ups, opening up the possibility of detector side-channel attacks. These optical beams also suffer from spatial aberrations due to atmospheric turbulence and unfavorable weather conditions. Consequently, we introduce a measurement device-independent (MDI) QKD implemented with vortex vector modes. We study the transmission of vector vortex and scalar beams through a turbulent atmospheric link under diverse weather conditions such as rain or haze. By utilizing the vector vortex beams, which has largely been ignored in the literature, we demonstrate that a maximum secure key transmission distance of 178 km can be achieved under clear conditions. When raindrops have a diameter of 6 mm and fog particles have a radius of 0.5 $\mu$m, the signals can reach 152 km and 160 km, respectively. Since these distances are comparable, this work sheds light into the feasibility of implementing MDI-QKD using vortex vector modes and opens the door to long-distance quantum secure communications.