Living Lands says: "All Forests are 1/1 creatures that are still lands". I assume these lands are colorless? So they could still block a creature that had protection from green or protection from colored spells or whatever?
Yes, the Forests will almost certainly be colorless.
Living Lands only changes the types, power, and toughness of those Forests. It does not change their color at all, so they will retain whatever colors they had previously.
Lands are almost always colorless, even the basic lands, so they'll stay colorless as Living Lands animates them. A Forest might produce green mana, but it's not green itself.
Since they're colorless, something with protection from green won't have protection from the colorless 1/1 Forest creature.
If the lands have colors for some reason, they'll retain those colors as they get animated. For example, Arixmethes, Slumbering Isle is a blue and green land before it wakes up. If it's somehow animated by Living Lands (perhaps you also have Yavimaya, Cradle of Growth) it'll keep those colors.