How taxes support the military is decided by lawmakers. We vote candidates based on their programs. If a candidate promised to lower contributions to defense, (s)he'd have my vote. You can have labour that doesn't feed the military.

You're technically correct. If we subscribe to a morality based on causal links of one's actions, then you'd partially responsible for the actions of your government, when paying any taxes to them. If they're involved in a war, so are you.

However, even in "peaceful" countries you'd have a hard time avoiding that, as most of them have some sort of mandatory pensions system, who in turn most likely fund arms production, which will then sometimes be sold to be used for war.

My logic included an explicit allowance for those people whose best career decision is to work for the military (or for the police, or the TSA, or whatever). I don't expect a general strike, no matter how much I want the workers of the world to lose their chains.

So the same logic would be okay with people where all reasonable career decisions require working for a company that pays taxes to the military, and both Matt Cutts and I seem to be in that situation. But I think we're both in the situation where we have plenty of reasonable options other than working for the military directly. And it specifically sounds like he took an option that is worse for him personally, because he thinks it's better for the world. I disagree it's better for the world, simple as that.

(Whether this logic would forbid working for companies that support the military indirectly is an interesting question, and I think 'BinaryIdiot has convinced me that it should.)