RE: yes!!!
Early in the season it's usually mostly females on the rocks I hoop, later after a few storms it turns to almost all males.
Normally when I hoop I release all females, but early in the season if that's all I'm getting I'll take a few females under 3 pounds.
I don't keep big females, the larger their tales the more eggs they can carry and protect. There's plenty of bugs out there and you can only eat so many lobsters so it's not big deal to let a few go.
All legal lobsters are breeding age even a small female carry's hundreds of eggs. In contrast any male can breed with several females so I don't feel bad about removing males (even large ones) from the population.
Oh.... and yes... Full moons are bad for hooping if your in clear shallow water. The bugs see the shadow of the boat and are more skiddish. When the moon is full I use longer ropes and always come in from down current. You don't want your shadow getting close to the net before you start pulling it, or the bugs will bail.
Jim