Siman 385

A Tzadoki—he is like an Israelite and may nullify his domain, and even though he desecrates the Shabbat in matters of rabbinic law—they are under duress, for the custom of their fathers is in their hands. (Magen Avraham, subsection 1) However, his eruv is not effective, since he does not believe in eruv, for the essence of the eruv is that he must resolve in his heart that his dwelling is in the place of the eruv, and he does not believe in this. And the Cutheans, the Samaritans—they are like complete non-Jews, and there is no remedy for him except through leasing. And an Israelite who is a transgressor regarding idolatry or to desecrate Shabbat in public, even if he only desecrates it with a rabbinic prohibition—he is like a non-Jew, and there is no remedy for him except by way of leasing and not through nullification, and certainly not through an eruv. And if he desecrates in private and not in public, even if he desecrates it with a Torah prohibition—he is like an Israelite and may nullify his domain. However, his eruv is nothing, when he does not believe in the eruv.

An Israelite who became a transgressor and had houses in an Israelite neighborhood that made an eruv for the entire year, if he has no other entrance at all except through the Israelite neighborhood—behold, he prohibits the eruv on every Shabbat that occurs after he became a transgressor. However, if he has another entrance to a neighborhood of non-Jews, even if the entrance was small and he was not accustomed to it previously—nevertheless, we push him toward this entrance that is open to the neighborhood of non-Jews, so that he does not prohibit for them. And this was in ancient times, when Israelites lived in a neighborhood by themselves. But in this time—he cannot prohibit the entire city, for in the entire city we rent the domain. But the courtyard in which he lives—certainly he prohibits, and it is necessary to rent from him his domain in the courtyard, if the courtyard is made into an eruv by itself. But when it is included in the entire city—nothing is necessary, for regardless we rent the domain, and automatically all are included from whom we need to rent the domain, and against his will he is nullified to the entire collective of the city. (So it appears in my humble opinion)