A CEO's leanings are relevant when they are clearly stated, and inspire a large part of his strategy -- to take a similarly controversial subject in the US, imagine the CEO of a gun-maker “against weapons”; that would come off as hypocritical.
I don’t think that there is such a thing as being “against weapons” though. Some people don’t think that one should profit from the use of deadly force; in that case, not using a significant portion of that company’s profits to repair damages from misused weapons would be callous. In most cases, weapons manufacturer are direly aware of the issue with what they sell, and try to make better quality devices to prevent them. Namely, a policeman friend told me that Glocks (could be another brand, I know very little about firearms) were appreciated by her colleagues who do a lot of pursuits because they don’t tend to accidentally fire when they drop from their holster, a rare but potentially tragic event. Glock makes money from that fear, hopefully invest to mitigate it.
I know government processes better, and as someone who could be seen as a socialist, I agree with Musk on one thing: government is expensive. Unlike him, I think it’s generally cheaper than private companies or charity. However, in the industries where Musk operates (transport), his entrepreneurial talent makes his contribution much cheaper. He doesn’t like public money to be wasted — that’s his publicly stated “political leanings” and one that has motivated SpaceX existence. I don’t think it’s very controversial, actually (no one likes to waste money) but it is relevant. What he asks for is to have the ability to lower it.
Therefore: yes, his leanings matter. In that case, and probably a majority of his projects that are government-funded, they are so because it is cheaper to have Musk’s company do it. Which is good. I’m not a US tax payer, so I shouldn’t care so much, but I would say: there isn’t a contradiction with trying to improve what you think is broken. If he was asking to prevent competitors from entering the market for government-contract, there I could see an issue.
