The effects of high concentrations of clay stabilizers in drilling and fracturing fluids on wellbore flow safety and natural gas hydrate exploitation have gained recent interest. This study investigated the effects of different concentrations of inorganic polymer, alkali, and silicate clay stabilizers on the phase equilibrium of methane hydrate at experimental mass concentrations of 2, 5, 10, and 15 wt %. The inorganic polymer clay stabilizers employed are zirconium oxychloride and polyaluminum chloride, the alkali clay stabilizer is potassium hydroxide, and the silicate clay stabilizers are potassium silicate, potassium methyl silicate, sodium silicate, and sodium methyl silicate. The clay stabilizers caused the phase equilibrium curve of methane hydrate to shift to higher pressures and lower temperatures and exhibited different degrees of thermodynamic inhibition. The average temperature drop ranged from 0.09 to 9.28 K, and the inhibition effect increased with concentration. The inhibition effect of the inorganic polymer clay stabilizers on methane hydrate was the weakest, while potassium hydroxide and sodium methyl silicate exhibited the strongest inhibition ability. The hydrate samples were also characterized in the presence of the clay stabilizers by powder X-ray diffraction, Raman spectroscopy, and cryo-scanning electron microscopy. The clay stabilizers did not alter the crystal structures of the hydrates, but they did affect the occupation of methane molecules in the 5(12)6(2) hydrate cage. The hydrates on the sample surfaces were distributed regularly under the influence of the electrolytes, which also confirms the inhibitory effect of clay stabilizers on hydrate formation.