Does a creature with protection from white take damage from a white creature with trample?

Protection from white means the protected creature cannot be damaged by white sources, cannot be enchanted/equipped/fortified by white things, cannot be blocked by white creatures, and cannot be targeted by white spells or abilities. This is summarized by the mnemonic DEBT (Damage, Enchant/Equip, Block, Target). CR 702.16e states that damage that would be dealt to the protected permanent by a white source is prevented.

When a white creature with trample attacks and is blocked, the attacking player must assign lethal damage to each blocking creature before assigning any excess trample damage to the defending player (CR 702.19b). However, if the blocker has protection from white, any damage assigned to it by that white trample creature is prevented by CR 702.16e. The trample damage that 'tramples over' to the player is still dealt normally, since the player does not have protection.

Importantly, the trample damage assigned to the blocking creature does not simply vanish and redirect — it is assigned there and then prevented. The attacker cannot reassign that damage to the defending player. CR 702.19b requires lethal damage to be assigned to blockers first, even if that damage will ultimately be prevented.

Example: A 6/6 white creature with trample attacks. It is blocked by a 2/2 creature with protection from white. The attacker assigns 2 damage to the blocker and 4 to the defending player. The 2 damage to the blocker is prevented (protection), but the 4 trample damage still hits the player normally.

So the protected creature itself takes zero damage from the white trampler, but the defending player still receives the excess trample damage. The protection only shields the creature, not the player.