Does a replacement effect that prevents damage also prevent deathtouch from being applied?

Deathtouch works by making any amount of damage dealt by the source lethal to the creature or planeswalker it damages. However, this only matters when damage is actually dealt. Under CR 702.2c, a creature with deathtouch causes any nonzero amount of damage it deals to be considered lethal damage.

The crucial link is CR 119.3: damage is 'dealt' only after prevention and replacement effects have been applied. If a replacement or prevention effect reduces damage to zero (or redirects it entirely), no damage is dealt at all — and deathtouch never gets the chance to apply (CR 614.1a, 615.1).

So if a creature has protection from black, and a black creature with deathtouch attacks it, the protection prevents all damage (CR 702.16e). Because zero damage is dealt, the defending creature will not die from deathtouch.

Concrete example: Your 1/1 creature has 'prevent all combat damage that would be dealt to it this turn.' An opponent attacks with a 1/1 with deathtouch. The damage prevention effect fires (CR 615.1), damage is reduced to zero, zero damage is dealt, and your 1/1 survives — deathtouch does nothing because there was no damage event.

Note the condition: if damage is only partially prevented and at least 1 damage is still dealt by the deathtouch source, deathtouch does apply to that remaining damage (CR 702.2c). Full prevention stops deathtouch; partial prevention does not.