I guess...uh...that it'd be less dense, so that'd dick up tides on Earth.

https://nssdc.gsfc.nasa.gov/planetary/factsheet/moonfact.html

Mean density (kg/m³): 3344

https://eurekamag.com/research/001/061/001061121.php

At 8 deg C, mean densities of blockformed and conventionally-hooped cheeses were, resp., 1.094 and 1.091 g/ml.

So that's 1094 kg/m³.

Basically, Earth's tides would be about a third as strong, which I imagine would affect a bunch of things, especially coastal ecology. Dunno how much tides affect weather.

Also, probably alters the reflectivity of the Moon, so would affect the brightness of the Moon. Might affect a lot of nocturnal critters and such. Hard to estimate, since that depends a lot on what cheese is involved.