I've seen very dark gray mortar, as well as red mortar. Just like brick, there's a wide variety of "correct" colors. While you're looking at brick colors, pay attention to the mortar as well.

Red Brick + Black + White. Britt Design Studio. Stick to a classic color palette for a timeless look. This New Jersey home is a new build that looks like it has been there forever, ...

Lime produces an off-white mortar. The patient person mixes and tests the mortar before committing to using it. You mix some up, lay a few bricks, and let them sit for a month.