Grease is basically a soft carrier which holds a lot of a base oil in suspension. The carrier used to be either a soap or a clay - which is why you see the reference to light metals in different types of grease. Different metal ions are how different soaps and clays are formed. Soaps and clays both are compounds of aluminum, lithium, barium, calcium and so on. For example, different light metals give you different kinds of clay - bentonite, illinite, montmorillinite, kaolinite and so forth. Same for soaps.
Incompatible greases happen when two different carriers react to form a solid. Then the oil is squeezed out . You may have seen this same thing happen on old grease or grease which is stored at high temperature - The grease tubes will actually drip oil until it has none. So add age or temperature to the list of grease problems.
Then along came polyurea as a carrier. Tests showed it should hold the base oil better & longer. There are two main families of polyurea - called "conventional" and "shear stabilized". Conventional poly had compatibility problems. The newer shear stabilized polyurethane is compatible with just about every other grease carrier chemistry. That's better, but the shear stabilized costs more....of course....
I know this stuff from some industrial work I used to do, but I still don't know the perfect answer. And even if we did, there is no assurance in today's world that one batch is like another.
What I do is use John Deere's tubes of shear stabilized polyurethane TY6341 grease just about everywhere. It's general purpose & also happens to be green - but I don't know if that is because the material is that color or if they dye it. It's always available & medium priced. No problems so far.
The one kind of place I use something else is on dirty low speed & very high load bushing surfaces like the backhoe swing tables or the lower FEL bucket pivot. Those get a sticky molybendum grease - usually a lithium base, but there I'm looking for moly plus tacky plus a higher viscosity base oil.
Your opinions welcome,
rScotty