Do Rainbow Cichlids Eat All Plants Or Just Some Plants?

[Joller]

i'm thinking of getting a rainbow cichlid, only last time i had these i remember they ate all my plants
fortunately i only have 2 plants now, a lily (which will probably die over winter) and an anubias(i think)
does anyone have any experience with rainbows and thicker types of plants? would they eat it?