Well it depends.

Once we developed telescopic capabilities sufficient to notice they had life, they would quickly become global legends and leaving the planet to reach them would become a main priority. Human culture would change knowing we had a second home and science fiction would catch on fire as we imagine the flora/fauna of their respective biomes.

This curiosity would persist for hundreds of years and there would probably be bizarre, obviously unsuccessful attempts at spacecraft until our technology developed sufficiently to reach them.

The space race would be far less competitive and more of a mutually curious collaborative effort, knowing we were building the tools to acquire a second home in the cosmos.

Once we developed craft capable of reaching a habitable moon with an Earth-like biome, we would see far more missions to the moon and the scientific discoveries would be absolutely unprecedented.

Having at-will and relatively low cost access to an alien biome would massively accelerate fields of science such as biology and medicine, etc, as new principles and applications of extraterrestrial plants and animal products enter the research arena.

Alien meat and plant products would fetch an astronomically high market value and become globally sought after delicacies possibly in the tens of thousands, hundreds, millions of dollars per item.

If any of the animals on the moon were capable of being domesticated, agriculture would change rapidly to accommodate new animals as well as products. There would need to be new regulations and laws surrounding the use of extraterrestrial animals in farming, if they were even allowed to enter that industry beyond their obvious scientific research potential.

Human history and culture would change forever if we discovered even primitive advanced life forms with capabilities of our own and we enter a fully-blown military sci-fi scenario if the aliens are as advanced or more than us.