There is a video circulating from the shiva home of the family who suffered a horrific, unthinkable tragedy over Chol Hamoed הי"ד. A Chasidishe Rebbe comes to be Menachem Avel and the avel asks him to say Hallel on Yom Ha'atzmaut.
He elegantly [in fluent English] didn't answer "no". That would have been untactful and impolite and the Rebbe is I am sure tactful and polite [ESPECIALLY when trying to console a man whose life has just been shattered forever]. He instead related how much his Zeide, a previous Rebbe, loved Eretz Yisrael and cleaned its streets [after making a Neder to do so when forced by the Nazis to clean streets] and that we have to love all Jews. Then Hallel will come on its own [meaning, I guess, that Moshiach will come and we will say Hallel big time]. Ad kan divrei Ha-Rebbe Shlita.
This brings us to a larger theological and Halachic question. Namely, does our Creator want us saying Hallel on Yom Ha'atzmaut? The secular Zionists don't say Hallel because they don't daven [so at least they don't say תחנון either]. The religious Zionists say Hallel .... religiously. The so called "Charedim" don't say Hallel for numerous reasons. One is that the State and its founders were a declaration of rebellion against Hashem, His Torah and our heritage. Ben Gurion [and his cronies] was a kofer in everything and one of the only aveiros he wasn't able to do was "לא יזח החושן מעל האפוד" and to shecht a korban with מחשבת פיגול. But a large percentage of the other aveiros he did. His declaring a State that would be conducted not in accordance with tradition in the Holy Land is not a reason for Hallel but for [as some actually say] kinnos. Of course, in retrospect many great benefits, both material and spiritual, have been attained due to the existence of the State but also many many great חילולי השם have occurred. If one loves Hashem it is hard not to feel immense sorrow over the latter and simcha and gratitude for the former.
So nobody is minimizing the magnitude of the suffering and loss of this poor man. May Hashem give he and his family the strength to get through this and flourish. But that doesn't change the stance of the Chazon Ish, Brisker Rov and many many other luminaries [the rule among Gedolei Torah with notable exceptions] who didn't see the birth of the State as reason for a Yom Tov. [Rav Kahaneman, the Ponivitcher RY, had the Israeli flag flying on the roof of the Yeshiva on Yom Ha-atzmaut but was far from being what would be defined as a "religious Zionist". He was a "religious Torah-ist"].
המוציא מחבירו עליו הראיה. In order to say Hallel it must be proven from our sources that it is desirable or obligatory. By a person's dress and address you can usually tell what he thinks about the issue. I would add that by the Charedim they don't talk much about it. It is not even a question. So there is much literature about it that emanates from the religious Zionist world but almost none from the Charedi world. The two groups follow the same Torah and same G-d but have a very different perception of those two "categories".