Is there a reason that Americans now pronounce luxury "lugsury" instead of "lucshury" while still pronouncing "extract" and "extra" with the more common "x" sound?
As David Garner mentioned in a comment, "extract" and extra" wouldn't be pronounced with a /g/ sound because the x is before /t/ in these words.
The letter "x" is sometimes pronounced with /g/ + a voiced fricative sound when it comes before a vowel; mainly when the following vowel is stressed (as in exact). In luxury, the following vowel is not stressed, but in the related word luxurious, it is. So it seems likely that the pronunciation of luxury with /g/ is derived from the pronunciation of luxurious with /g/. I don't know why there would be a difference between British and American speakers. As was mentioned in the comments, not all American English speakers use /g/ in luxury: some use /k/.
There is a common practice to smooth words out in American English. Some smoothing are not problematic and don't diminish from the general acceptability of the sentence such as "lugsury" or "jewlerry". They are written off. But then there are occurrences like "liberry" and "nucular" that make people sound uneducated.