I'm new to this site, and to the whole SE network in general, so my concepts relating to tags may be slightly skewed. And in offering my 2¢ worth, I might be due some change. Still...
I do think the christianity should to be replaced or renamed, as the case may be, to christian instead, as mentioned here. Most of the other mythos-related tags have the understood "myth" or "mythology" in them. For example, there is japanese for Japanses mythology, greek for Greek mythology, and norse for Norse mythology. There are few tag for the religions themselves, such as Odinim, Dianism, or Zoroastrianism.
The christianity tag may be a rather large umbrella due to the diversity of denominations that fit under that heading. I don't know if other schools of thought, including the Greek mythologies, have such a large range or not, yet there are very few, if any, that have/had a single, undivided mythos.
I also don't think that adding new-testament or old-testament is necessary. No more so than the need for poetic-edda and prose-edda, which exist. The bible tag should be good enough to cover both new- and old-testament questions, and questions of other purportedly related writings. I would even suggest that it should be used to cover the other "sacred texts" of the Christian realm, including the Book of Mormon, the Pearl of Great Price, the Doctrine and Covenants, and the Dead Sea Scrolls, as well as all the various "version" and "editions" of the Bible, from the Authorized King James Version, to the New World Readers Edition.
I think the "catch" here is that tags are a classification and serching tool, not a solution. The tags help to group things that are related, and filter out what is not related. If the tags are split too fine we end up with lots of tags with only a pair of questions that have no natural connection to others that are naturally related. The title of the question should be where the differentiation, if any, occurs. In the question itself is where the OP should create the filtering information that can be searched from the main site.