It's infighting among party insiders. Since their branding is the plucky underdog who speaks truth to power^TM, it doesn't politically benefit them at all to publicly commit to a side since they would essentially be siding with a faction of insiders. Right now, there's no clear winner, so that also carries the risk of siding with an eventual losing faction and facing swift reprisal from the future winning faction.

In the end, they lack political clout and influence to actually swing a particular faction they want in their favor. From the perspective of the faction that they are supporting, their support is completely useless, meaning they will not be rewarded for their loyalty. From the perspective of the squad, their support just puts a giant bulleye on their backs. They will most likely be aloof and dodge all questions asking them what faction they support until the very end where they will join the winning team to demonstrate that they don't really oppose the winning faction or support the losing faction(s).