If a creature has protection from a color, can it be equipped with an equipment of that color?

Protection from a color grants four key shields, remembered by the acronym DEBT: the creature cannot be Damaged, Equipped/Enchanted, Blocked, or Targeted by sources of that color (CR 702.16b). The 'E' explicitly covers Equipment: a creature with protection from a color cannot be equipped by an Equipment that is that color.

When you try to attach a colored Equipment to a creature with protection from that color, the equip ability is countered, or if the Equipment would become attached through another effect, it simply cannot be attached and remains unattached. CR 702.16b states that a permanent with protection 'can't be equipped' by sources of the specified quality if those sources share that quality with the protection.

It is important to note that most Equipment cards are colorless (artifacts with no color indicator or color-granting ability), so this situation is less common than it might seem. However, some Equipment do have a color — for example, an Equipment that is white due to a color-altering effect or by its own nature — and those would be blocked by the appropriate protection.

Concrete example: You control a White Knight (protection from black). Your opponent controls a black-colored Equipment (imagine an Equipment enchanted by a black Aura that makes it black). Your opponent cannot attach that Equipment to White Knight; the equip ability is countered on resolution because the creature has protection from the Equipment's color.

If the Equipment were colorless, however, protection from black would not prevent it from being attached, since the Equipment is not a black source (CR 702.16b, 301.4).