On the other hand, with regards to Yom Yerushalayim, they do seem to imply that Hallel should be said on sunday morning, not Monday. Would the same logic not apply to Yom Ha'atzmaut?

The rabanut gets its knickers in a twist all the time over this. What happens when yom haatzamaut is postponed to 6 Iyar will we then not say tachanun on youm hazikaron?

Our last Yom Hatzmaut before making aliyah Yom Ha'atzmaut was celebrated on 6 Iyar. Someone told the Rabbi that we shouldn't be saying Tachnun because it was 5 Iyar. The Rabbi said no problem, but that means we will say Tachnun tomorrow. The request was quickly dropped.

It seems to me if this was a straight up halachic question the Rabbanut should easily come up with a consistant guidelines to come up with their answer. They have had 64 years to come up with a final answer.

Isnt yom atzmaut just a choose for yourself type of thing?
I have heard the following minhagim:
half hallel
whole hallel w/o bracha
whole hallel w/o bracha, but be yotze someone else's bracha
whole hallel with bracha

shabbos pesukei dezimra
regular pesukai dezimra

haftara with bracha
haftara w/o bracha (not sure which one)
haftara, but only when there is torah reading
haftara even w/o torah reading

are you allowed to get a haircut?
yes - its a chag
no - even though its a chag, the hair cut will impact the aveilus aspect of the rest of sefirah

Based on rafis letters, which day can you get a haircut, assuming you can?

And my personal favorite, that quasi lecha dodi sung to the tune of hatikvah at night at the YA tekes.

This is a holiday that promotes unity among everyone - except chareidim. With all these minhagim, you would think that the chareidi approach of no hallel would be accepted, and not frowned upon.

These people think davening is in their hands to do with it whatever they want. Say Tachanun, don't bother with hallel. If you feel happy that the state of israel exists, thank g-d in your own way. There is no halachic way to justify this hallel business, even if the state of israel would be a positive thing for the jewish people.

-please note that the first letter is unsigned - no name, signature, or stamp at the bottom. makes you wonder who wrote it, and under what (lack of) authority.
IMHO, the vagueness on what tefillot are involved is presumably a product of the ambivalence of many involved in the Rabbanut these days to the day - an unfortunate fact that does not add the the honour of the institution in recent years.

- the second letter is consistent with the takanot of the rabbinate from the early years that the day should be moved to prevent hillul shabbat. (A fitting takana IMHO when you consider that the mandate actually ended 6 Iyar, but the declaration of independence was moved up to the afternoon of 5 Iyar to avoid hillul shabbat).
There were differing opinions, but this was the decision, and this is what is done by the praying public. (פוק חזי מאי עמא דבר)
-even though the day is moved, 5 Iyar still maintains a status as a "no tahanun day". There are also responsa that maintain one may shave for shabbat fri as it is 5 Iyar - I believe it was Rav Zvi Pessah Frank in Har Zvi, but I would have to double check.
- this approach was not universal, and when the issue of yom yerushalaim on fri or sun came up, the approach taken was different, to move the celebrations and not the prayers. I believe this was a function of the Rabbanim involved in the decision, as well as the unfortunate fact that yom yerushalaim was not declared a national holiday with massive celebration, so it was more feasible to shift a few events from one of the day to the other.
moadim lesimha legeula shlema.

The comparison to hallel on leil haseder is ridiculos, on pesach it was instituted by great tzadikim, hallel on 5 iyar was just to fill a political cause. Besides, the minhag of most israelis is not to daven at all, so why hallel on 5 iyar, perhaps shachris?....