There is not enough lore that explains why Aerith has green eyes. They look like the result of exposure to mako energy, like the SOLDIER members and other Shin-Ra experiments. Some theories state that she might have suffered from mako exposure throughout life. One example to support this is the opening scene of Final Fantasy VII Remake, where Aerith is staring at a leaky mako pipe. However, we do not have enough flashbacks which would prove that she had any other eye color in the first place other than green.