No table or sun visor limitation in the AFM (but did not check now). So that is the certifying authority stance.
Next step would be to check OM-B. Most operators use FCOM (modified so some extent) for this.
AFAIK OEM FCOM says table is to be stowed for tkof/ldg. Nothing about the shades.
I was told only once by a trainer that the shades need to be stowed up.
BTW: the 737 operator I worked for had a pre-start checklist item: sun-visors -> stowed. Is this a Boeing item?