Here are my comments in regards to the post and comments of Christopher over at The Church and The Liberal Tradition.
You state "I'm resistant to what I think is a reckless characterization of America as some kind of 'Masonic experiment.'" Well, regardless if you admit it or not, it's still a "fact," which you must sooner or latter admit to. Do some reading of both Catholic and non-Catholic sources my friend, which were provided to you in the comments on one of your earlier posts.
Brother, I beg you, the next time you visit D.C, open your eyes, OPEN your eyes. The entire city was designed by Masons (layout of the streets, all the significant buildings, memorials, White House, Capital Bldg, etc.). If the founders were so intent in making the physical structure of our nation's capital Masonic, is it not reasonable to assume that Freemasonry also influenced their beliefs & therefore their writings? Read any number of a dozen plus books I referenced to you and then let's chat.
To compare Muslims to Freemasons is not proper. In short, study what the Church teaches about Freemasonry. For example (one of hundreds), Pope Leo XIII in his encyclical letter Humanum Genus (1884) equated Freemasonry with the Kingdom of Satan. Study what any number of saints had to say about Freemasonry, i.e. St. Maximilian Kolbe, etc. Refer to what the Sacred Congregation for the Doctrine of the Faith (B16 himself) had to say about Freemasonry in 1983. The list goes on and on...
In regards to prayer, I recommend the following books.
Prayer: The Mission of the Church by Jean Danielou
Prayer by Hans Urs von Balthasar
World of Prayer by Adrienne Von Speyr
With God and With Men: Prayers by Adrienne Von Speyr
In regards to religious freedom, John Courtney Murray, and the Second Vatican Council, I recommend anything by Dr. David L. Schindler on this topic. The ROP articles (not on-line, but being snail-mailed to you) written by Baxter, Novak & Schindler are excellent, in addition to one of Schindler's Communio articles, which is on-line.
A few additional points...
Whalen's book is a good start, but it should not be the end. Another book that you might consider reading is directly below.
Behind the Lodge Door
My recommendation would be to study both Catholic and non-Catholic (even Masonic) books. There is no one perfect book on this topic. Study everything you can get your hands on, either at the library or buying used books, etc.
To my knowledge (and I could be wrong here b/c I'm not a historical theologian) the Church has never condemned the deity of Muslims. Muslims worship God the Father (excluding the Son and Holy Spirit). The Church has taught very clearly about the deity of Masonry and it's none of the above.... It's the devil.
Which leads to the following point and I'm not the first to make it. It is this - Errors in the understanding of who and what God (or more appropriately god) is for our Masonic Founding Fathers (Washington, Jefferson, Franklin, etc.) led to errors in many other areas of their thought, including their understanding of religious freedom, which are spelled out in our governing documents. The logic of the Founding Fathers is a mixed-bag of Masonic, Enlightenment, and classical principles. I refer you to Kraynak's and Craycraft's books on this topic.
Schindler in his various pieces (as mentioned above - the Fall 1998 issue of The Review of Politics & the on-line article from the EWTN library plus Chapter One of his book.) gives a strong critique (very nuanced) of Murray's thought on religious freedom and that of our Founding Fathers.
In regards to your last paragraph... What exactly do you mean by the "God of America"? There is only One God for all of mankind regardless of what individuals may choose to believe... Some have a more fuller understanding than others, i.e. Catholics. The "God of America" is the Lord Jesus Christ, but that doesn't mean the founding documents of our country are not full of erroneous principles derived from Masonic and Enlightenment thought.