If Kirk’s exhortations to the Organians are to be taken at face value, life in the Klingon empire is pretty brutal for non-Klingons.
Is there any reason to believe things have changed by the time of TNG, or does the alliance with the Federation help the Klingons to brutally enslave other worlds?
In “In the Pale Moonlight,” when Sisko talks of the “safety of the Alpha Quadrant,” is he really just referring to the safety of the Federation, outside of which there are few worlds that are really free? It seems to me that for most of the worlds in the Alpha Quadrant, what is at stake is that they will be enslaved by the Dominion if the Dominion wins the war, or continue to be enslaved by the Klingons or Romulans if the Dominion loses.
The Trek books often deal with this issue; debates as to whether Federation alliances with Klingon or Romulan are moral, whether peaceful co-existence can influence the empires into change or whether the empires will influence the Federation. Vulcan-Romulan reunification often touches on this, as does pretty much any Federation-Klingon relations story. Of course, the Klingon and Romulan states are never portrayed as "evil", and there have been several stories that give at least a hint of what life is like on subjugated worlds. The Klingons assign conquered people the status of Jeghpu'wI
, less than citizens, more than slaves. The Romulans enslave some races- Remans for one, obviously- but others appear to have similar status to Klingon subject races. Overall, the answer often seems to be that it is far preferable to make peace and co-operate with the empires, and influence them that way, rather than attempt to force change, which never works and causes further problems. Also, remember there are plenty of worlds that are independent, neither Federation nor part of a wider empire.
PS: A particularly interesting empire from Trek literature is the Regnancy of the Carnelian Throne from the novel "The Buried Age". Here, worlds symbolically accept slavery to the Carnelian Throne, symbol of justice and noble strength, and "play along" with conquest.