The Syndicate and the Super Soldier aliens from season 9 are two separate groups. The Syndicate is destroyed in Season 6 episode arc Two Fathers/One Son by the rebel aliens. After this happens many of the surviving members go underground and continue a counteroffensive attempt to stop the alien invasion but nothing much comes of their attempts. When Mulder is then abducted in Season 7 and returned in Season 8, the plot shifts to being one of the aliens preparing for invasion and replacing humans with the alien/hybrid counterparts also known as super soldiers. These are they who want Mulder dead because he poses a true threat to their ultimate goal.
EDIT: some additional reasons why the Syndicate wouldn't want Mulder dead
Members of the Syndicate disagreed on the "Mulder problem" throughout the series. The Martyr effect was a common reason given for keeping Mulder alive, usually from CSM as he was always protective of Mulder due to the fact that he was in fact very likely his father (there is much debate on the validity of this). CSM and other members of the Syndicate also helped Mulder in his quest because they wanted the truth to be known but couldn't openly come out against the pact they had made with the aliens. The Syndicate worked with the aliens to help prepare for invasion, but many of them also secretly worked to find a cure for the black oil virus, which would ultimately help them stop the alien invasion. Mulder was a key player to this second agenda.
This question has been on my mind as I've been rewatching the series in preparation for the new episodes. As I was watching the Season 1 episode "E.B.E." last night my ears perked up at the following dialogue between Mulder and Scully.
SCULLY: So they created this elaborate show just to deflect us again.
I mean, wouldn’t it have been easier just for them to –
MULDER: Just to kill us? Yeah, I wondered that myself. Maybe they’re
using me against myself like you said before. That I want to believe
so badly that I’d just accept the obvious conclusions and walk away.