Short version: I treat money market funds as safe money, although technically it's not 100% safe.
Technically, a money market fund can lose money. But 99.9% of investment firms have eaten losses rather than panic their clients. The losses tend to be small, and cause really disproportional panic. Investment firms do not want these funds to lose money. Newer regulations may challenge that, by trying to "float" the rate and allow it to go negative if the short-term rates go negative. My guess is even then, investment firms will flaunt the regulations to keep their clients happy, and eat the losses.