This chart from MachineryLubrication.com illustrates the compatibility between most grease types with three categories: compatible, borderline compatible and not compatible.
The decision to make a lubricant change within a machine should always be carefully evaluated. With greases, as opposed to oils, it is especially important to be cautious when switching from one lubricant type to another.
The decision to use a new grease in a machine must be managed with grease compatibility in mind. Whether two greases are compatible will depend on the thickener type and base fluid as well as the resulting grease properties after the two grease types have been sufficiently mixed.
(Read Noria's entire article, "Understanding Grease Compatibility"...)
