How do they make translucent caulk?

Or clear shampoo? Clear Sealant? Clear toothpaste?

After you’re finished mixing the chemicals, what do you add to make it translucent?

Many silicone polymers are naturally clear or translucent. Pigment or fillers are added to make it opaque. Clear shampoo is primarily a solution of a low molecular weight salt (sodium dodecyl sulphate) in water. Most salt solutions are clear, you only get cloudyness when you add compounds that are large enough to scatter visible light. Some examples of this type of material are proteins, starches, mica flakes, titanium dioxide, or detergents that form large micelles.
Clear toothpaste usually contains a naturally translucent colloid, such as Sodium Carboxmethyl Cellulose, as the basis for the gel. You don’t add anything to make it clear, rather, you refrain from adding anything that will make it cloudy.