Ann is a geologist and the ideological founder of the Red movement, an environmentalist stance that believes Mars should be left in its pure and natural state. To terraform the rusty-red planet is to destroy it and replace it with something else—this thinking runs counter to Sax's notion that Mars will still be Mars regardless of what humans do.
Ann persists that humans are not the "lords of the universe" but rather just "one small part of it" (6.3.125). And if we aren't the lords of the universe, should we act like we are by destroying and creating just because we can? Ann says no, but apparently a lot of people disagree with her because she ultimately loses the terraforming debate.
We should note that her philosophy comes with a double-edged axe (which is just like a double-edged sword only not one). As she studies the Martian geology, she must live and travel on it, resulting in her altering that landscape, too. Oops.
Granted, she doesn't alter the landscape to the degree Sax wants to, what with his meteors and atmospheres and such. As Ann tells Nadia, "But when […] I change [Mars]—I destroy what it is, what I love in it" (3.5.162). In the end, Ann's viewpoint can't accept change and so is doomed to tragedy as everything changes. Bummer.