^Right. Every nation has its dissidents, and we know from Paths of Disharmony that the people of Andor are split into numerous factions. So until it's made explicit, we can't know whether the Andorians working with the Tholians represent the current ruling faction or a fringe group.
The evidence
would seem to suggest that, between the skeptical government at home and the reluctant crew, Zhrar's embrace of a Tholian alliance is problematic.
At the very least, though, even if Zhrar's alliance with the Tholian is one that he struck with the Tholians and isn't a reflection of Andorian official policy, this still has major implications for the Andorians. It's the same sort of problem for the Andorian government that Sela's support of attacks against the Federation caused for the Romulan government: if Zhrar's actions are authorized by the legitimate governing bodies of his polity, either at the time or retroactively, they indicate that Andoria has gone strongly anti-Federation; if Zhrar's actions are unauthorized or even contrary to official policy, the Andorian government is weak enough that it cannot prevent its military leaders from striking their own deals with other powers.