Suppose a faction rises to political power, and subsequently imposes their will without regard for the claims of others in society. This looks to be an abuse of power. Why? I'm tempted by the following answer: political legitimacy requires that the State be sufficiently responsive to reasons. If it were not relatively reliable, it would have no claim to authority, for legitimacy attaches only to procedures that have an appreciable tendency to generate substantively good outcomes. (Cf. Estlund on Epistemic Proceduralism and the analogy with the jury system.) But to be unreceptive to others' arguments is one obvious way to lack the requisite sensitivity to reasons. The closed-minded exercise of power is thus inherently illegitimate.
(It's worth noting that such illegitimacy can arise even in a democracy: the "tyranny of the majority" is a very real threat in a democratic society where first-order sectarianism commands greater loyalty than metapolitical values. So it is not enough for a polity to hold elections and empower the majority. Much depends on the manner in which this power is wielded. In particular, a legitimate democracy must be guided by a widespread commitment to pursue the common good in co-operation with all others who share this commitment.)
I think the problem with dogmatic sectarianism is not just epistemic, though. There also seems to me something important about the idea of civic respect, i.e. respect for the capacity of other agents to contribute to collective decision-making. I'd be curious to hear what readers make of the following argument (which I first offered in comments elsewhere):
1. (Legitimate) Politics is the collective endeavour of co-existence, i.e. deciding together how we are to live together.
2. Receptivity and civic respect are preconditions for this collective activity.
3. Dogmatism is inherently illegitimate in the political sphere.