In some circles there is and I think that stigma is a cruel MISTAKE unless the person staying at home literally does nothing. Most stay at home moms and dads do a LOT of things that many people avoid. However, I do know of two ladies that stay at home, their kids go to school, hubby goes to work, and they do nothing. No cleaning, cooking, running errands, home repairs, etc.
Hubbies come home to filthy homes, screaming kids, and they have to clean up, fix dinner, run errands, etc. The men are not happy but live with the stress of it. Non-contributors should have some kind of shame for doing nothing with their lives and not contributing to the household. But, there should be no stigma attached to stay at home moms and dads.