The soldiers duty to refuse to carry out illegal orders such as slaughtering civilians notwithstanding, yes I think volunteering to fight for your country, even in an unjust war, is service.
The saying goes that the fish rots from the head down. There are stops all down the chain of command that could prevent soldiers from fighting unjust wars, and that’s where the blame should lie.
Sadly the US military has a lot of corruption and pushing back on a CO or refusing an illegal order can end your career in the military or worse. That doesn’t mean I blame the people at the end of the chain, I blame the people at the head. This includes Obama’s illegal drone strikes on targets in Syria and Yemen and various other atrocities and not just Trumps latests