Does a land with the basic land type Plains tap for white mana even without the basic supertype?

Under Comprehensive Rule 305.6, any land with a basic land type (Plains, Island, Swamp, Mountain, or Forest) automatically has the corresponding mana ability, even if that land is not a basic land. The 'Basic' supertype and the basic land type are two entirely different things.

The mana ability is granted solely by the subtype, not by the supertype. CR 305.6 states that each basic land type causes the land to have a specific intrinsic mana ability: Plains grants '{T}: Add {W}', Island grants '{T}: Add {U}', and so on. This ability exists on the card as if it were printed there.

A common example is Sacred Foundry, which has the subtypes Mountain and Plains. Even though it is not a basic land, it can tap for either {R} or {W} because it has both of those basic land types. Similarly, a non-basic land granted the Plains type by an effect (such as Blood Moon's counterpart Urborg, Tomb of Yawgmoth giving Swamp type) gains the mana ability immediately.

The 'Basic' supertype matters for other rules, such as the deck-building rule (CR 100.2a) that allows more than four copies of basic lands, and for effects that specifically search for or reference 'basic' lands. It does not gate the mana ability.

In summary: if a land has the subtype Plains, it taps for {W}. Full stop. The Basic supertype is irrelevant to this ability.