Shimon, Israel seemingly like US spends 5% of GDP on defense. Government budget (collected thru taxes) is at most 50% of GDP, so 10% of budget is for defense. This does not include other defense-like costs – police, FBI, maybe protection of cities near the border in Israel, etc.
In addition to defense, there are many other “pareve” things government spends on – roads & bridges, pensions and help to poor, at least basics. I think if you are fundamentally opposed to a country, you should find a way to get out of that country and live somewhere where you feel comfortable paying taxes. This is exactly what Rambam suggests, and if not “go to the desert” as Hazon Ish suggested … I can see, for example, if you are a citizen of Iran, North Korea, or Russia – a part of your taxes will be spent on murdering people, and even 10% might make one uncomfortable. So, it is OK to feel this way towards Israeli government, and it is entirely possible nowadays to move to another country nearby or further away.
This is like you come to a restaurant – and they you don’t like the food or even the kashrus. It is OK to go to another place, but not OK to eat first and then say you are not paying because it was burnt and treif.