Are the References to “God” in the "Pledge of Allegiance" Considered “Public Neutrality?”

I don't see how it could. I thought the church and state were supposed to be separate, isn't the statement "under God" in the "Pledge of Allegiance" doing the opposite? When it was originally written in 1892, by the socialist minister Francis Bellamy, there was no mention of "God," it simply read, "I pledge allegiance to my flag and the republic for which it stands, one nation, indivisible, with liberty and justice for all." Later in 1923, the words "the flag of the United States of America" were added. The pledge still did not include "under God," that wasn't added in until 1954. Many would and do argue that the words have no religious connotation since federal law, state constitutions, and US currency already contain references to "God." What I don't understand is why the words "under God" were added; the minister who wrote the original pledge didn't even put it in, based on the fact that this was to be solely a patriotic pledge. I feel that with the addition of "under God" religion and patriotism were confused and therefore, took away--possibly still takes away--the "public neutrality" schools are supposed to have, since children are to say the pledge every morning before school begins. Does the addition of the phrase still affect the "public neutrality" of the school setting? I think it might, in saying the pledge the children seem to be pledging allegiance to not only their country, but also to "God." In Clark's Naturalism vs. Supernaturalism: How to Survive the Culture Wars, he states, "the liberal-democratic political solution to the problem of coexistence is to keep the state ideologically neutral, creating a public space of secular services and protections base in no particular cosmology or view of human nature." From this I gather that the words "under God" should not have been added to the "Pledge of Allegiance," for it takes away "public neutrality." However, this is still just a personal opinion.

(This site lists many pros and cons to the argument of "under God" and "public neutrality" in the "Pledge of Allegiance" http://undergod.procon.org/)