Naive pluripotent stem cells (nPSCs) frequently undergo pathological loss of DNA methylation at imprinted gene loci, posing a hurdle for biomedical applications and underscoring the need to identify underlying causes. We show that nPSCs from inbred mouse strains exhibit strain-specific susceptibility to locus-specific deregulation of imprinting marks during reprogramming and upon exposure to a mitogen-activated protein kinase (MAPK) inhibitor, a common approach to maintain naive pluripotency. Analysis of genetically diverse nPSCs from the Diversity Outbred (DO) stock confirms the impact of genetic variation on epigenome stability, which we leverage to identify trans-acting quantitative trait loci (QTLs) that modulate DNA methylation levels at specific targets or genome-wide. Analysis of multi-target QTLs on chromosomes 4 and 17 suggests candidate transcriptional regulators contributing to DNA methylation maintenance in nPSCs. We propose that genetic variants represent biomarkers to identify pluripotent cell lines with desirable properties and may allow the targeted engineering of nPSCs with stable epigenomes.