Growing up a Seventh-Day Adventist, I never heard anyone boasting about canceling their newspaper subscription, but I hear this from Jews all the time (particularly the Modern Orthodox who are hyper pro-Israel). I guess they feel it is social proof of how pro-Israel and ethnocentric they are and you can never suffer within your group for such chauvinism.
The New York Times is the best English-language newspaper in the world and its left-wing tilt is easy to spot and to take into account when you try to understand their articles.
Jewish Journal Editor Rob Eshman nails it in his five questions column:
4. Are you aware the New York Times unsigned editorials are consistently pro-Israel? “There was no way Prime Minister Benjamin Netanyahu was going to tolerate the Hamas bombardments, which are indiscriminately lobbed at Israeli population centers,” reads a July 18 editorial. “Nor should he. As President Obama said on Friday, “No nation should accept rockets being fired into its borders, or terrorists tunneling into its territory.” What part of that do you find offensive?
5. You say in conclusion that you don’t expect your cancellation will matter to the Times at all. Then why do it?