Can we specify Phosphate Texture?

Is there such a thing as "smooth" vs. "rough" phosphate? We have a phosphated part that is pushed into anther part. The "rough" finish increases the pushing force.

Yes, you can by asking for a thinner coat.
A better way is to chose your type of phosphate.
Manganese is very coarse and rough, but is wonderful for break in and holding lubricants.
Zinc phosphate is finer, but if parameters are not closely controlled can get to be very needle like. My preference is a calcium modified zinc phosphate. It is quite uniform and smooth. Thickness is easy to control and can be quite heavy on a grit blasted surface vs a pickled surface.
Iron phosphate has virtually no corrosion protection and is mainly for paint adhesion.
Cost may be a factor as well as your desired use.