To what extent is grease interchangeable?
Some greases really are special. But in other cases the grease doesn't really matter. Since so many companies just say to use their approved grease, it can be hard to tell apart which applications are really special and which ones don't really matter.
There are some applications where you should only use the approved grease and using the wrong grease really will cause a problem. This includes roller brake grease. This is critical to use the exact grease specified, and unsafe to substitute anything else.
Also, some frame couplers specify special fluoro-compound grease, and it's best to follow the instructions or potentially ruin your frame from thread galling.
Any carbon parts like carbon seatposts should use grease recommended by the manufacturer or for the application.
Internal gear hubs usually use oil, but it's important to use the correct lubricant. Some hubs like the NuVinci hub literally are designed around the special oil they use. For other hub types, the grease doesn't usually matter.
On the other hand there are a lot of applications where the grease doesn't matter that much. In that case I use boat trailer bearing grease, or if something lighter or cleaner is needed, white lithium grease. These include things like most steel threads including pedal threads, steel seatposts and quill stems, brake pivots, wheel and headset bearings, crank splines, cassette splines, etc.