I’m not well versed in grease so I don’t have a technical reason. But I use Valvoline synthetic and any name brand synthetic in the past. With seeing the old dried up nearly nonexistent grease chunk out in pieces, or old watery grease pour out of old joints when disassembled, it seems like having actual useable grease is more important than brand.
totally makes sense just swapping in new axles. It’s ideal. Regrease is an option for unavailable options, keeping a back up, or for those already doing more than average axle work with lifts or off-roading.