Newton rings are a result of almost full contact betwen two smooth surfaces. The distance between the two surfaces must be of the same order of magnitude as the wavelength of light! When light is reflected between the two surfaces, some of it will be half a wavlength (or one and a half, or two and a half...) out of step with that passing directly through. This had the same result as absorbing a little of the light.
The distance between film and glass, especially around a speck of dust, will vary from practically zero to a number of wavelengths. In between, all colours of light will be "extinguished" at some point. This is what gives Newton rings.
It does not depend on humidity, but on the "shinyness" of the surfaces.
So the two ways to combat it are: A: Increase the distance, or B: Increase the roughness.