Washington state is the third most populous state west of the Mississippi (being beat by only Texas and California), and probably has more farmland than Ireland, though it depends on what you mean by small farm.

I think the biggest issue I have with the comparison is the density. Ireland is a relatively densely populated country. Rural land is very densely populated, there is no section of the country that isn't spoken for. This is because unlike large parts of the US, agricultural land is highly productive without irrigation. This results in agricultural land being very expensive. In the US agricultural land can be expensive, but only because of it's water. Without water it's extremely cheap. This land pressure results in land across the entire Country being expensive. In the US, there is a lot of relatively empty/undeveloped land on which to build houses and cities. This should reduce the price of housing.

- in contrast to rural Ireland, urban Ireland is not very dense relative to other cities in Europe. Dublin has a height restriction on buildings (which may be being reconsidered) so there isn't much of the denser building that you get in cities like Paris (which has a lot of 5-6 story buildings which really ramp up the population density. Irish cities are instead rows of very tightly packed suburban homes - often terraced or semi-detached (sharing a side wall with a neighbor) with about 6-10 homes per acre.

I'm not following your analogy at all. Ireland is 32k square miles, Washington state is 72k square miles. Washington State has about 16% more people with about 2.25 times the land area.

There is a biiig mountain range in the middle of the state