One who adheres to religious practices approved by authority or tradition
n., pl. -im
A person who dissents from officially accepted dogma. A heretic.
An Orthoprax Kofer is the guy who believes in nothing, yet goes to shul and keeps shabbos out of habit, or for fear of his wife and neighbors. He does the dance, and talks the talk, but, inside, he thinks it's all nonesense. Teaneck and Woodmere, havens of Modern Orthodoxy, are thought to overflow with such people.
But what about Williamsburg and Boro Park? Granted, the average black-hatted longbeard doesn't think "its all nonesense" but all the same, many are koferim, per the Rambam who ruled that whoever denies even one of the 13 principles is a heretic. Teaneck and Williamsburg might not be denying the same principles, however both have their difficulties with some of what the Rambam taught.
What follows is a quick review of the famous principles, together with a discussion of how the different neighborhoods deny them -- stereotypically speaking, of course, because life - not to mention this post - is too short for anything but generalizations.
1. God alone has made, does make, and will make all things.
Pockets of the Modern Orthodox world do accept evolution, but very few deny that God is the First Cause.
2. G-d is One. There is no unity that is in any way like His. He alone is our G-d He was, He is, and He will be.
3. G-d does not have a body, physical concepts do not apply to Him. There is nothing whatsoever that resembles Him at all.
In Williamsburg, many believe that God has emotions like joy and anger and that He can be changed through prayer. It is also believed that He desires prayers and the performance of mitzvoth, and that he can be consoled through the acts of man. All of this denies the third principle. Though pockets of Teanek make this mistake, too, my opinion is its more common in Williamsburg.
4. G-d is first and last.
Somewhere in the back of my head, I have the idea that Hassidim hold that God created the wrold from eternal matter. I have not encountered this myself, though, and I don't know how common it is.
5. It is only proper to pray to G-d. One may not pray to anyone or anything else.
Ancestor worship is common in Williamsburg. Many pray to their dead and ask for intervention and favors. Some of the slichot and other prayers are directed to angels. Per the Rambam all this is heresy. (Again, we find this in Teaneck, too, but to a lesser extent, Slichot that pray to angels for example are largely ommitted in MO shuls.)
6. The words of the prophets are true.
7. The prophecy of Moses is absolutely true. He was the chief of all prophets, both before and after Him.
8. The entire Torah that we now have is that which was given to Moses.
Teaneck is more familiar with biblical archeology among other subjects, and are therefore aware that this is not plausible. (They also know that the Rambam himself, surely, did not believe it, and neither did the Ibn Ezra, the Rashba or Rabbi Moses Sofer.)
9. The Torah will not be changed, and that there will never be another given by G-d.
Well, in Williamsburg they do say that the rules about proper prayer times were abrogated, but we'll give them the benefit of the doubt, and presume the law was changed legitimately.
10. G-d knows all of man's deeds and thoughts.
11. G-d rewards those who keep His commandments, and punishes those who transgress Him.
Yet, many believe that God rewards people who wear red bracelets, for example, or other amulets. These and other superstitions abound in Williamsburg, and all, per the Rambam are heresy because it denies the idea of reward and punishment.
12. The Messiah will come.
13. The dead will be brought back to life when G-d wills it to happen.
Teaneck 3: Williamsburg 1