I assume the religious dog tags in question, whether being bought for people or dogs, are being purchased privately. Why? My own 30 years of Federal service and knowledge of our secular environment considers it unfathomable that any Federal government agency would purchase obvious religious items for official use.
As personal items, if a higher court rules that religious dog tags are allowed by the U.S. Constitution's First Amendment freedom of religion clause, then all religions would be protected, not just Christianity.
Personally, I want freedom from all false religions since they offend both God and me, but as a Christian and American who believes in the First Amendment as interpreted by the Foundng Fathers who wrote it, I tolerate the presence of false religions and respect an individual's right to follow them so long as they don't hurt others by their actions.
Now here's a final response to your last question that will certainly draw oppostion from those here who don't respect our nation's Christian heritage. Written documents firmly demonstrate that our Founding Fathers established America as a Repubic based upon Christian beliefs and Biblical moral values. The Federal government supported the Christian religion extensively, starting with its first act of funding production of a new American Bible, establishing a juresprudence system based upon the Bible, and establishing a public school system for the purpose of reading the Bible. Understand also that many of the States had designated churches that were actually funded by the governments. There was no Constitutional separation of church and state as interpreted today until Hugo Black's Supreme Court Ruling in 1947 where he misinterpreted and canonized Jefferson's phrase.
Yes, I would support government/public funds being spent to advance the Christian faith as was done for the first 300 years of our nation. Sadly, I recognize that our society has turned it's back on having God's hand in the nation's affairs, as well as embracing Christianity and Biblical moral values. I believe America's on a downward spiral, and reclaiming our Christian heritage is the only thing that will save it.