Newton Rings are based on light inference between the glass and the negative. They can only appear, if there is a tiny air space between the glass and the negative. If the surface of either the negative or the glass is not absolutely smooth, the air between the glass and the negative can escape and both get into real contact. The emulsion side of the negative is usually not very smooth. So Newton Rings may not appear on this side.
The structure of an Anti Newton Glass or of a Mylar (or other diffusion material) is usually not rendered below mag-ratios of ~25x. However, they reduce contrast transfer in theory when the diffusion is between the neg and the lens.
Any diffusion above the neg may change the light characteristics in case of a condensor head. But did you really experience any Callier Effect with your negatives? IMO, this requires point light sources and super fine emulsions to really matter. I did not find any non-linear difference between my diffuse/diffuse densitometer and my lab mether below the condensor head. A diffusion may change contrast transfer, but I would not expect any non-linear changes here.