When starting from dry, there is little worry. I prefer Lithium based grease, as it repels water better than the Sodium types. Add some moly and the wear is reduced even further.
But some greases don't mix well, meaning that the capability of the grease is reduced below the basic properties of either. So, it is not recommended to put, say lithium grease, where sodium grease is installed. This doesn't apply if ALL the previous grease is removed before adding a different base type.