Marx first lecture
A. Why is Marx writing about "the Jewish question"? The question (as considered by Bruno Bauer) is about political emancipation of Jews in a state with some form of Christianity as established religion. (Marx sarcastically says that the German state in which the question arises is "no state as such … a theologian by profession" [p. 98].) In North America church and state are separated, and Marx clearly sees this as a mark of increased political maturity. Here (he might say) we have a real state, not just a theologian. (Political life is emancipated from being structured by religion.)
B. But religion is still practiced (now in private), and Marx says (p. 100) that "the existence of religion is the existence of a defect." Why?
1. He thinks religion is "the opium of the people" (p. 115).
2. More specifically: taken out of politics, religion becomes "an expression of the separation of man from his communal nature" (p. 104).
C. To see his point, consider the structural parallel involving private property (p. 101). Here too, when e.g. property qualifications for voting are abolished, that leaves private property still structuring another region of people's lives (no longer their political life). This is life in "civil society" as opposed to life in "the political community" (see p. 102). In this life a person "acts as a private individual, regarding other people as means and degrading himself to the level of a means" (p. 102). Marx sees private religion as similarly expressive of egoism (presumably he takes it to express a concern with one's personal salvation). But it seems plausible that "life in civil society" is more significantly shaped by the sort of social and economic factors he illustrates with the case of private property. Religion is only an excuse for discussing the "contradiction between the political state and civil society" (p. 105). [In fact one might, consistently with Marx's basic thought, defend (some) religion on the ground that it bonds rather than separates.]
D. Human beings are (in principle) "communal beings" or "species-beings": unique among animals in being able to recognize themselves as sharing their species-nature (humanity) with other members of their species — a special potentiality that can't be realized except in contact and cooperation with others. This conception of human nature is the principle of the mature political community. The "contradiction" is that in life in civil society a human being seems to give expression to a nature as "an isolated monad withdrawn into itself" (p. 108). And it's easy to think that's real life, so that's a human being's real nature; the idea of life as a communal being comes to look like an other-worldly abstraction. (See pp. 102-3, 114.)