Does protection from multicolored prevent damage from a gold card with a single color pip?

Protection from multicolored means the protected permanent or player cannot be dealt damage, enchanted/equipped, blocked, or targeted by sources that are multicolored (CR 702.16). The key is what 'multicolored' actually means in rules terms.

Under CR 105.2 and CR 202.2, a card's color is defined by its mana cost color indicators, or characteristic-defining abilities — not by its card frame or the 'gold' aesthetic. A card is multicolored only if it has two or more colors (CR 105.2b). A card with a single color pip, even if it has a gold frame or is colloquially called a 'gold card,' is simply monocolored.

So: if a card has only one color pip (e.g., a hybrid card with just {R/G} that makes it both red and green, or a card with only a single {R} pip), you must check how many colors it actually has. A card with a single non-hybrid pip like {R} is monocolored. Protection from multicolored would NOT prevent its damage.

Concrete example: You control a creature with protection from multicolored. Your opponent attacks with a creature that costs {2}{R} — it has one color (red) and is monocolored. Protection from multicolored does nothing here; the damage goes through normally. However, if that creature cost {R}{W}, it would be multicolored and protection would prevent the damage.

The 'gold card' frame is a visual design choice and has no rules meaning. Always check the actual colors of the card as defined by its mana cost or color indicator (CR 202.2, CR 105.2).