Do basic land types affect a card's color identity?
No, you may not include lands with basic land types that produce mana outside your commander's color identity.

Land with basic land types have innate mana abilities. While this makes them a special case among all cards, these abilities are not reminder text and do have an effect on gameplay.


  305.6. The basic land types are Plains, Island, Swamp, Mountain, and Forest. If an object uses the words “basic land type,” it’s referring to one of these subtypes. An object with the land card type and a basic land type has the intrinsic ability “{T}: Add [mana symbol],” even if the text box doesn’t actually contain that text or the object has no text box. For Plains, [mana symbol] is {W}; for Islands, {U}; for Swamps, {B}; for Mountains, {R}; and for Forests, {G}. See rule 107.4a. See also rule 605, “Mana Abilities.”


That seems to indicate that cards like the Triome (land with basic land types, no other abilities with colored mana symbols) have a colorless identity and thus could be included in any commander deck, because the innate ability is granted to objects, rather than cards. 

However, for such cards, there is a special rule that looks at the color of mana they could produce.


  903.5d A card with a basic land type may be included in a Commander deck only if each color of mana it could produce is included in the commander’s color identity.


So no, you could not include Indatha Triome in your Elenda Dusk Rose commander deck, because it produces {G}.