That a species-culture is at odds with the UFP, or has declared outright war, is not a major hindrance to a member of that species-culture serving in Starfleet. Indeed, heightened tensions might result in an increase in dissent, treason and defection, making the UFP welcome members of totalitarian, specieistic enemy cultures in its own ranks for propagandist purposes. After suitable loyalty checks, of course.
Romulans in Starfleet are only unlikely because of the lack of contact with, or indeed knowledge of, them. And that's not an issue in the Kelvinverse where Romulans appear a thoroughly known quantity in 2258 at the latest. Other species or cultures might have other special hindering factors - the Jem'Hadar might die of malnutrition before completing basic Starfleet training, say, or the Ocampa of old age before completing command studies. Klingons... probably don't suffer from any special hindrances. After all, Worf, a supposedly average full Klingon, didn't.
Timo Saloniemi