Back when I was teaching auto mechanics, we had a fairly long series of lessons on lubricants in general, and grease in particular. All "grease" is made up of at least two components, plain old lubricating oil, either mineral based or synthetic, and "soap" which gives it enough stiffness to stay put. Some soaps aren't compatible with others, something that can pose a problem with wheel bearings in particular. Since it's not practical to clean all the old grease out of things like tie rods, ball joints, etc. there might be a situation where radically different base greases might not play well together. Other than that, if it's good and slippery and stays put without leaking out, no problem!
Jerry
