There are several areas in which I disagree with religious Judaism as a whole and there are areas which I agree.
One very major area that I disagree is the way they justify Torah and the Talmud. You can see some of the arguments in books by Rav Avigdor Miller. These arguments in favor of Torah and Talmud are obviously false. On the other hand I do have a way of arguing negatively for Torah and Talmud.
That is I can’t justify what I will call now just "Torah" [but meaning Torah along with it commentary the Talmud] in a positive way but I can deal effectively with most of the criticism. This I do mainly based on my readings in philosophy of Kant, [non intuitive immediate knowledge--which is meant to work mainly for a priori knowledge.], and the Intuitionists like G.E. Moore and Michael Huemer. 
So in short I do justify Torah but not in the way of the Orthodox.


There are individual areas of halachah I also disagree but these are based on my reading of the Talmud and the later authorities like the Rif, Rambam, Tur, and Shulchan Aruch with its commentaries the Shach and the Taz.--




Specific areas of disagreement are the time of Rosh Chodesh, electricity, some aspects of Nida, and the status of statehood of Israel and serving in the IDF. But in general I accept the general framework of Halacha and how a legitimate halacha opinion is found and defended by means of the Talmud and poskim that I mentioned above. In other words I claim that a halacha that can't be defended by the Talmud is not a legitimate halacha.


In terms of Books in Torah thought that I think are the most impressive I would have to put the  the Madragat Haadam of Joseph Yozel Horvitz commonly known as the "Alter of Navardok".
As for the Madgarat Haadam there is not even any English translation.

I think both of these books can provide a system of checks and balances in Torah thought. For each one on its own can be misused. But both together I think provide a very good approach to Torah.


Some of the most important ideas in these books a re ideas that have universal validity and are in no way specific for Jewish people. One is trust in God with no effort. This is probably the most important idea of the Madragat HaAdam. The other is talking with God in a forest or some place far away from other people. 



The Orthodox do have one advantage over me--they seem more Jewish.This seems to me to be the result of a kind of nationalism (or rather chauvinism)  in which seeming Jewish seems to be the most important thing. And the Orthodox certainly seem very Jewish. They wear lots of black clothing. They speak Yiddish. They hate everything that smacks of  culture or gentile thought. There is obviously nothing remotely good or Jewish about any of this. But if what you value the most is to seem Jewish, then by all means go ahead and join them.




The thing I should mention about non intuitive immediate knowledge and how it helps to justify Torah is this. One basic area of debate between the rationalists and the empiricists is this we can know things  based on empirical evidence. because we can check our conclusions with what happens in the real world. But when it come to a things that we perceive by reason alone things  how do we know that what we think has anything to do with reality? [This is a bit of a simplification-- we do find the intuitionists think that even empirical evidence we know only by reason].
It is this question that immediate non- intuitive knowledge comes to answer.
It does more that just answer Kant's question how is synthetic a priori possible. It answers how is a priori possible.

Once you get to synthetic a priori we can see that there are areas of value that we know beyond just the principle of non contradiction. and we can test these areas by falsification. In other words even morality which we cant derive from an "is", we can falsify . This is what Socrates spent all of his time doing. and this is in large part what the Talmud is doing. Except the Talmud accepts  sources of information that were unknown to Socrates.