If it can be shown that this whole exercise was/is essential and critical to defeating Islamist terrorism, that would be grounds for support.

There are in fact precedents (IMO) for the justified invasion of another country, by the way. In 1978 Vietnam invaded pesky and aggressive Cambodia (Kampuchea). Pol Pot got overthrown in the process. Anyone object to that?

However, the human cost (as you point out) is incredible. Let's see how this thing develops over the next few months. Now that this thing is a fait accompli, I'm just hoping the US/Coalition forces will succeed in stablizing the situation and reducing the suffering.