Well, I would assume that you mean anomalous data like that purported in the book Forbidden Archeology by Michael Cremo. I would argue that those apparent anomalies need to be critically analyzed to see if they are genuine anomalies, and then you need to look for other similar anomalies. There's good reason to doubt the authenticity of most archeological anomalies. After the time of Darwin, they did a lot of for profit expeditions, and a lot of it was motivated by the desire for fame or money, so there were many bunk discoveries that were purported as being significant. But the more reliable discoveries and data, which doesn't have reason to be doubted, and is better documented, is generally what scientists prioritize. Anomalous data is marginalized until there is enough evidence to validate it. So, I think modern archeology and anthropology is generally reliable, but then all knowledge is only conjectures, never absolute, so you have to keep that in mind. There's a lot we don't know, will never know, and simply can't know.

As for physics, that's just a big can of worms. With a lot of it, there's just no theory to make sense of the data as of yet. I mean, all of quantum mechanics and theoretical physics has to do with reconciling pretty big anomalies, so I don't think there's too great of a tendency to ignore anomalies.