From the article:
Oshri published his findings in the journal Archaeology in 2005, two years after he completed the dig. He said that Protestants were open to it, but those who are more orthodox in their beliefs, such as Catholics and the Greek and Russian Orthodox, were not willing to accept his ideas.
http://www.timesofisrael.com/was-jesus-born-in-a-different-bethlehem/
I do not think that the reason is that they are more or less orthodox, the simple explanation is the huge amount of money and prestige invested in the http://en.wikipedia.org/wiki/Church_of_the_Nativity
The church is administered jointly by Greek Orthodox, Roman Catholic and Armenian Apostolic authorities, thus they will never accept any other location.
This http://thejewishhome.org/counter/BethlehemOfGalilee.pdf is a good text that as well includes the work by Oshri http://archive.archaeology.org/0511/abstracts/jesus.html
Thanks for the thoughtful replies, and Merry Christmas to you!