I know this is belated, but I thought readers would find this interesting. There are many views on this subject, but R. Ahron Soloveichik’s is one that tends to get overlooked. The following is from his book Logic of the Heart, Logic of the Mind:
Before turning to the halachic questions raised by Yom Haatzma’ut, we must ask whether 5 Iyar, the day on which the independence of Israel was declared, is of more significance than any other day in the course of our survival in the War of Independence. I think it is… (p. 188)
There is no doubt that Hallel cannot be recited with a blessing today. (p. 191)
The recitation of Hallel is obligatory only when the redemption affects the Jewish nation in its entirety, and this will be realized only in Yemos Hamoshiach. (p. 196)
In other words, Hallel is optional on Yom ha-Atzma’ut but, if recited, should not be said with a berakhah. I distinctly remember that when he prayed in the YU beis midrash, he would say Hallel in its “proper” place while everyone else was saying tahanun.