The spatio-temporal intra- and interspecific competition of two diffusing similar populations is considered. The growth of both populations is either logistic or shows an Allee effect. Conditions of spatial segregation without mixing are investigated. Furthermore, the impact of density-dependent environmental noise on the occurring stationary fronts is studied. A special focus is set on the development of functions describing the density-dependent noise intensity. The obtained results are associated with a biological case study related to the competition of two invasive weeds.