The Dishonorable Mr. Worf

[Kobayshi Maru]

Since Errand of Mercy, we see Klingons are able to respect other races.

The blood of all Klingons has become water. Since the Federation alliance we have turned into a nation of mewling babies. Romulans are strong. They are worthy allies. They do not turn Klingons into weaklings like you. - J'Dan in The Drumheads
J'Dan wasn't the only Klingon to think that. Klingons are extremely proud, but the respect the other one who's valuable. Some Klingons think the Federation is valuable, some others believe the Romulan Empire is way more valuable.

The Klingons have all sorts of people, some reasonable, some extremists. We've seen that in the series and the movies.