I used a Xantrex 3624 modified sine wave with a house fridge for years with no issues. Not only me but lots of RV'ers. I would be leery of a small cheap MSW, but have no experience with them.
Some refrigerators today do not have coils they use the sides and top to dissipate heat and need space for air to circulate around them to cool, check instructions.
Many products today claim to use the best material and design and manufacturing techniques possible. But then say in tiny print that if you use the product the warranty is void.