Magnetism in transition-metal dichalcogenide monolayers has attracted considerable attention, yet its nature remains elusive, particularly in monolayer 1T-VSe₂. Our first-principles calculations show that Stoner instability can drive ferromagnetism in XS₂ and XSe₂ monolayers (X = Ti, V, Co, Mo, and Ru), associated with a reduced density of states at the Fermi level. We demonstrate that mixing nonmagnetic Ti, Co, Mo, and Ru disulfides or diselenides can induce magnetism. Conversely, mixing magnetic VS₂ or VSe₂ with other compounds can completely suppress magnetism. Both scenarios can lower the total energy. Moreover, substituting a small number of V atoms with Co defects can also disrupt ferromagnetism in 1T-V(S,Se)₂. Even in pristine 1T-VSe₂, we find ferrimagnetic configurations with reversed local V moments that are nearly degenerate with the ferromagnetic state. Their competition may contribute to the suppression of long-range ferromagnetic order. This reduced energy penalty for magnetic and structural disorder arises from a suppressed density of states at the Fermi level, resembling the mechanism underlying the Peierls transition. Electronically driven energy lowering near the Fermi level may therefore be widespread among transition-metal dichalcogenide monolayers in various forms.