Easy in-universe reason for Vorta/Jem'Hadar Starfleet officers:
After the conclusion of the Dominion War, the "new" Great Link, influenced by Odo, sent representatives of Dominion member races back to the Alpha quadrant not to wage war, but to integrate with the Federation, the Klingon Empire, and so on.
After a time, and with the recommendation of Colonel (perhaps, with Bajor in the Federation, now Starfleet Captain/Admiral?) Kira and other high ranking officers, some of the Vorta and Jem'Hadar were admitted to Starfleet Academy.
I believe Kira is the new Kai (spiritual leader) and has no official standing in the federation.