Magnetic materials often exhibit complex energy landscapes with multiple local minima, each corresponding to a self-consistent electronic structure solution. Finding the global minimum is challenging, and heuristic methods are not always guaranteed to succeed. We apply an automated workflow to systematically explore the energy landscape of 194 magnetic monolayers from the Materials Cloud 2D crystals database and determine their ground-state magnetic order. Our approach enables effective control and sampling of orbital occupation matrices, allowing rapid identification of local minima. We reveal a diverse set of self-consistent collinear metastable states, further enriched by Hubbard-corrected energy functionals with U parameters computed from first principles using linear response theory. We categorize the monolayers by their magnetic ordering and highlight promising candidates for applications.