Pamela, I thought thought the similarities in the tartans was a conscious decision.
First, the dyes available in the 18th century were both fewer and less bright than those available today. The historical dyes were plant based; bright, colorfast chemical dyes were a Victorian innovation.
Second, I think the similarities in the tartans were a rebuttal to Murtagh’s remark in the stable scene. He’s worried that if the Red Coats see a tall, red-haired man dressed in Fraser tartan (“colors” as Jamie says) they’ll know it’s Jamie. But, in fact, I think the Brits wouldn’t have known one tartan from another. Tartans were less standardized then, the hunting tartans were less distinct, and we want to think those fops from The Garrison Commander episode were clueless about the lives of the Scots.