I don't think you understand how a defensive alliance works - being in NATO doesn't oblige you to join in a NATO member's pet war crimes project, it only obliges you to defend them if they're attacked on home soil. That's why it's such a powerful deterrent to somebody starting a war with a NATO member. So although obviously the US, UK, France or whichever is the warmonger du jour will obviously put pressure on you to join them in a war as their NATO ally, there's no obligation to do so unless they are attacked at home.
Even then, you look at somewhere like Turkey who I believe have been attacked in e.g. the Syria conflict and it hasn't automatically triggered the defence clause - there is some room for nuance and/or doubt as to the origin of an attack.