Is it permissible to send Tzedaka money to support the poor in Eretz Yisroel, or to hospitals in Eretz Yisroel, or, for example, to organizations in Eretz Yisroel who help handicapped children?
Is this allowed, according to the Torah; or is this considered supporting the Zionist state?
There is nothing wrong with sending them money. There is a difference between supporting Zionism and its state (giving to UJA, AIPAC, ADL, Israel Bonds) and helping individual Jews, even if some of them happen to be Zionists. All Jews are our brothers and we want to help them in their time of need. It is said that the Satmar Rav once gave a lot of tzedaka to the editor of a Zionist newspaper in Eretz Yisroel, who had to marry off his daughter and had come to him for assistance. The gabbaim tried to remind the Rebbe that this man had published many articles attacking him, but the Rebbe just called him back and gave him even more.