Dear Avira,
On yidishkeit. When a Yid does a mitzvah because he is a comitted Jew, that is the desired outcome of creation. This is even if the Jew has no concept of a creator or any idea of the god-head. Just the act itself, is included in ‘boruch asher yakum es divrei hatorah hazos’. Now, how can this be if the practitioner has no devotion to Hashem or his Torah?
The answer is exceptionally unique in the annals of mankind. Hashem gave the Torah to us! It really, actually happened. And now that it is here, it is the individual possession of every single yid and all of Yisroel’s collective possession simultaneously. So even when a mitzvos are done with no connection to Hashem, is is still Torah by the mere connection of being Jewish. Because even though the intentions and devotions are almost nil, it is unaltered Torah in that the practice itself is representative of what the Torah wants from us.
A look at the taryag will easily demonstrate that Hashem gave us the Torah for us to enact it by living it. Not much in the way of how we should devote ourselves or what our intentions should be. There are many ways to approach God. But there is only one mission to carry out on His behalf. All the sugyos that we learn, are filled with the smallest details of proper actions. There is no sugya of proper beliefs.
Even the most far out atheist, can be a committed Jew. Rav Hirsch said as much regarding Spinoza. And the Chofetz Chaim have avowed atheists mussar about keeping mitzvos. His sefarim are filled with admonishments about mitzvos that people ignore. But when it comes to belief, he just writes that the common belief is not at all the way the Torah views it.