The E’Y analogy does not work at all. There is an important distinction between things that are non-Jewish (i.e., things said, done, and thought by non-jews who have no obligation to follow our Torah) and things that are un-Jewish (i.e., things said, done, and thought by fellow Jews that are obligated to adhere to the Torah, but choose not to do so).
There is little inherent problem with associating or supporting things non-Jewish, but associating or associating with things that are un-Jewish, even if you do strictly adhere to the Torah, runs the risk of implicitly legitimizing a Jew’s break with halachah.
Satmer and many others have problems with the Israeli government because it is an un-Jewish institution. The State of NY, or the United States, or any other country for that matter is a non-Jewish establishment. Even when they go wrong, supporting and associating with them does not risk legitimizing the uprooting of Torah ideals. Any reasonable person should be able to recognize that the State of NY is not bound to follow the Torah, so if they adopt though legislation non-Torah morals this says nothing about what the Torah or Jews say.