The genetic identity of three mummies found in the Takla Makan Desert has been declared far and wide to be Celtic. But that's the popular press talking. There is not now, nor has there ever been, a common genetic marker that says "this person is a Celt." There are common markers amongst the Irish, not the least of which is for a blood disease in which the body doesn't process iron properly. But the Scots don't share it to the same degree. The Bretons and Welsh don't, either, let alone the Cornish and the Manx. The assumption of red hair marking a Celt is a fantasy, too, as red hair is more common amongst the Norse.
So what does that make the most embarrassing archaeological find the xenophobic Chinese government could imagine shy of discovering they were founded by time-traveling American capitalists? Most definitely genetically European. But that's as refined as it gets unless you're lucky.
As for the carvings, their similarity to continental Celtic designs makes perfect sense without assuming the mummies were refugees from prehistoric Aberdeen. It was noted years ago that the blatantly Caucasian mummies and wall paintings in the area were associated with the Tocharians, a culture that started up near the Ural Mountains and extended their reach along the Silk Road. The Ural Mountains are where a lot of the European cultures got their start, so design elements in common make sense. As for the fabric? Tocharians were Silk Road traders. The trade routes did not terminate at either end of that road; they branched out. Without clear evidence they had more than those pieces in that vicinity, it's quite a leap to claim they were from that part of the world. And the Scots were not the only people who wove like that then, either.
Their being Tocharians does put them right into the Indo-European matrix alongside the Greeks, Norse, and others. This means their burial traditions are useful to contemplate for possible common threads. Blue stones where coins normally go in some IE burial rites are still likely to be an offering for the conductor of the souls of the dead, for example. But Tocharian is not a Celtic language, and a few dolmens and spirals don't make them a Celtic culture.