First, I agree with Adam that you can use weighted averaging to deal with the moonlit sky, but I want to add a bit more to what he said. Moonlight adds sky glow, which adds an unwanted signal to the object and it raises the background level. The overall effect is to reduce the contrast of the image. You can always regain that contrast when you process the image but you do so at the expense of a decrease in SNR. That means that in order to maintain a given SNR, you have to increase the total exposure time. Signal weighting during stacking is the statistically correct way to deal with varying SNR across the stack but the net result is the same. So, take away number one is: If you want to achieve a high SNR when the moon is out, you need more exposure time.
Unfortunately, the moon doesn’t simply add an angle invariant brightness to the whole sky. As everyone knows, the sky is brightest near the moon, falling off as you get further away. But, there’s a subtle problem because the rate of brightness fall-off varies with 1+ cos²(theta) and with color due to the way that the atmosphere scatters with wavelength. (There are also some polarization issues but we’ll ignore that effect for now.) The daytime sky is blue because of Rayleigh scattering from oxygen and nitrogen molecules, which depends on the inverse wavelength to the fourth power. That inverse power of four strongly favors shorter wavelengths and is a powerful generator of color gradients. So, when you shoot RGB data with the moon in the sky, you are likely to get terrible color gradients—particularly if you shoot over many nights with the moon at different angles to your object. When you stack all that data, you will almost certainly find high-order color gradients that are challenging to remove. You’ll have a similar gradient problem with your Lum data but without the added problem of underlying color issues.
So, what to do? First, I shut down my RGB imaging efforts within about 5-6 days on either side of the full moon, and even then, I try to avoid imaging anywhere near the moon in the sky. Second, I’m okay shooting Lum data to within about 3-4 days of the full moon as long as I can maintain at least 40 degrees separation to the moon. Again, it’s important to take more Lum data when the moon is out and you’ll have to be prepared to remove gradients. So, if you are careful about how you manage it, you can shoot LRGB with a “fair” amount of moonlight.
John