Okay.. I skimmed ALL OVER the tutorials section and could not figure out how to fix this.
There is a tutorial on how to make things shiny... but I could not find one to do the reverse.
(I tried setting reflectivity to "none" and stdMatEnvCubeCoef to "0,0,0", (but all these settings were ALREADY on the non reflective state.)
My mesh STILL shines!

I started with the "Thickrims" glasses and imported a new mesh for a hat accessory. Everything works great except the hat has the same shiny look as the glasses frame did. I don't know why and cannot figure it out.

I'd like my hat accessory to not be shiny!

Try:

Reflectivity=1 (this is a weird thing, the higher the number the less reflective)

stdMatEnvCubeMode=none
make sure the stdMatEnvCubeTextureName has been deleted in both the properties and the file list areas.

ETA: I have used the above on objects and it works, but have not tried on accessories as I have only made earrings.

Thank you for the advice! I tried... but my hat is still shiny.
This is so weird...

Okay! I did it.

All I did was add"1" to the end of:
stdMatDiffCoef: 0.8,0.8,0.8

So after it was:
stdMatDiffCoef: 0.8,0.8,0.8,1

THEN I changed the "Type" in the cMaterialDefinition tab to:
"SimStandardMaterial" INSTEAD of the previous "StandardMaterial".

(While keeping reflectivity and everything else at 0 and none as written opposite to the "make clothing shiny/bumpy/reflective" tutorial).

I think this technique should be added to the accessory tutorials for people making none reflective accessories from glasses meshes.

AWESOMESAUCE!