I'm far from an expert on greases, but can add a bit to the discussion.
A grease has either an petroleum or synthetic oil base plus a thickener to keep it in place. Lithium, silica, and clay are examples of traditional thickeners. PTFE (Teflon) is a more recent one. Silicone can apparently be both a base (synthetic) oil and a thickener.
The higher the "NLGI" number, the thicker the grease. NLGI #2 is pretty common and it's about the consistency of peanut butter. There's more to this than just consistency though -- things like shear rate.
As an example, Nyogel 767a is a silica thickened NLGI 2 fairly heavy grease meant for damping. Compared to other NLGI 2 greases the consistency seems much more like putty (good if you want damping) than either the lithium or silicone based greases I've used on various instruments and machines.
What's wanted for optics, is something that stays put (a grease), isn't volatile (otherwise lighter fractions might condense on lenses), and is very resistant to oxidation over time. A combination of volatility and oxidation is what causes old microscope greases to harden up over time.
Personally, I'm not sure why a silicone based grease would be more likely to get all over anything than any other grease. I've heard both yes and no that's it's harder to clean off optics, though. Thankfully, haven't run that experiment yet on my own objectives, eyepieces, prisms etc.
McMaster-Carr (the industrial supplier) has a page on greases listing things like heat and water resistance and oxidation. I'd suspect that heat resistance is pretty well correlated with low volatility. Just looking at the McMaster quick guide, it looks like calcium sulfonate (an old standby for extreme pressure applications) might (?) be an ideal thickener for optical mechanisms, but at a cost.
Here (an an example) are the Nyogel 767a specs: https://shop.newgatesimms.com/wp-conten ... l_767A.pdf