Just imagine the equivalent in Christianity - a Pope allies with a heathen power for political gain in Italy. Just how long would he last before an anti-Pope is elected in his place
Except Rome, and its emperors, aren't comparable to the papacy, not yet at least.
For starters, the romans generally believed all people's God's were as real as their own. So merely working with the believers of other gods wouldn't automatically destroy someone's reputation.
Secondly, it was the duty of romans, but especially the emperor, to secure the blessings of the gods for the sucess of the state. So if working out a deal with british druids could stop their gods from opposing them, it'd be great. Of course, if human sacrifice really was a thing druids did, it would have to end for rome to be comfortable working with them at all.
And with regards to the druids political power, it definitely seems to me that they acted as judges, and learning the law by heart being part of their training. Thats in addition to the power they held as religious leaders. As mentioned before, they could exclude individuals from rituals and such, turning them into outcasts(or maybe even outlaws).
A lot of myths also have druids acting as advisers to kings/chiefs, which makes sense given they're legal experts.
That said, i don't think i ever saw anything about ruling directly, as a king would, so it may be that they were barred from such positions. But i don't think that would be too much of an issue.
As i said before, the Romans would prefer to have their own man in charge, and it seems likely that the britons wouldn't like being ruled directly by druids either.
So having a king of somesort, chosen by the emperor, with an advisory council of mostly druids and powerful chiefs/warriors, would be acceptable.
Britain would practically be a roman province, but without the costs to occupy and maintain it.
The britons maintain a degree of self rule, and enjoy the trade rights they get as a roman client/vassal state. And over time they'd come to adopt a number of roman customs and technologies.
Thats not to say there'd be no opposition, an either side of the channel, but its the most acceptable for most parties