I try to do my best to help raise consciousness with the words that I choose to use when I speak or write, whether it's substituting "humanity" for "mankind" or "child of Christian parents" for "Christian child". Recently, I was emailed by a Jewish individual who politely pointed out an interesting presumption behind the word "Judeo-Christian". Christianity may claim to share some things in common with Judaism, but the difference between the Christian god and the Hebrew god is the difference between polytheism and monotheism. Even in other areas where Judeo-Christian is often used, such as 'Judeo-Christian values', Christians seem to actually reject the Judeo portion.
For example, the ten commandments are argued by many evangelical Christians to be the Judeo-Christian foundation of our American legal system. But how many of these same believers will observe the Sabbath? The ten commandments are treated like a historical relic, and Christians will freely admit they are no longer under the old law, because of Jesus' sacrifice. Thus, the "Judeo" prefix seems more like an attempt to either be politically correct after centuries of Christian oppression of Jews or it's intended to give the illusion of something being generic, as opposed to strictly Christian.
In the case of the latter, it is especially relevant that "Judeo-Christian" has been almost exclusively invoked in the United States. Perhaps the reason for this may be the separation of church and state in our country. Many on the Religious Right seem to think that if something can be generally applied to all religions, it somehow does not violate the Establishment Clause. Hence, "Judeo-Christian" might be used to mask the truth of some issue being sectarian, or strictly Christian.
Of course, not all usages of "Judeo-Christian" are problematic. Referring to the emergence of Christianity, it may be well suited to consider some things as "Judeo-Christian" in the sense that they actually do have elements common to both religions. Early Christians who abstained from certain foods and still observed the Hebrew law can rightfully be called "Judeo-Christian", I think, as they were partially Jewish in their views. You'd be hard-pressed to find such types among Christians today, though.
While there are some appropriate uses for the term, I believe "Judeo-Christian" should be used more carefully. This probably isn't an issue for most people, but as a former Christian and ex-apologist, the word has lingered in my vocabulary. It does seem harmless too, which is all the more reason to bring these things to consideration.