Using density functional theory (DFT) calculations and the Greens's function formalism, we report the existence of magnetic edge states with a noncollinear spin texture present on different edges of the 1T′ phase of the three monolayer transition metal dichalcogenides (TMDs): MoS2, MoTe2, and WTe2. The magnetic states are gapless and accompanied by a spontaneous breaking of the time-reversal symmetry. This may have an impact on the prospects of utilizing WTe2 as a quantum spin Hall insulator. It has previously been suggested that the topologically protected edge states of the 1T′ TMDs could be switched off by applying a perpendicular electric field [X. Qian, J. Liu, L. Fu, and J. Li, Science 346, 1344 (2014)]. We confirm with fully self-consistent DFT calculations that the topological edge states can be switched off. The investigated magnetic edge states are seen to be robust and remain gapless when applying a field.