mozda da izaberete sami sta vam najvise odgovara :)
http://thesaurus.reference.com/search?q=like-minded
8 entries found for like-minded.
Main Entry: like-minded
Part of Speech: adjective
Definition: of the same mind
Synonyms: agreeing, compatible, in accord, in agreement, of like mind, of one mind, similar, together, unanimous, united

Main Entry: amicable
Part of Speech: adjective
Definition: friendly
Synonyms: accordant, agreeing, amiable, brotherly, civil, clubby, concordant, cordial, courteous, cozy, empathic, fraternal, good-humored, harmonious, kind, kindly, like-minded, mellow, neighborly, pacific, peaceable, peaceful, polite, regular, sociable, sympathetic, understanding
Antonyms: aggressive, hostile, nasty, unfriendly

Main Entry: compatible
Part of Speech: adjective
Definition: harmonious
Synonyms: accordant, adaptable, appropriate, congenial, congruent, congruous, consistent, consonant, cooperative, cotton to, fit, fitting, good vibes, good vibrations, groovy, in keeping, like-minded, meet, mix, proper, reconcilable, simpatico, suitable, sympathetic, togetherness
Antonyms: disagreeable, incompatible, incongruous, inharmonious, unsuitable, unsuited

Main Entry: concurrent
Part of Speech: adjective 2
Definition: agreeing
Synonyms: allied, centrolineal, coinciding, compatible, concerted, confluent, consentient, consistent, convergent, converging, cooperating, coterminous, harmonious, in agreement, in rapport, joined, like-minded, meeting, mutual, unified, uniting
Antonyms: contradictory, different, differing, disagreeing, in disagreement, incompatible

Main Entry: congenial
Part of Speech: adjective
Definition: friendly
Synonyms: adapted, affable, agreeable, amicable, clubby, companionable, compatible, complaisant, congruous, consistent, consonant, conversable, convivial, cooperative, cordial, delightful, favorable, fit, genial, good-humored, gracious, happy, harmonious, jovial, kindly, kindred, like-minded, mellow, pleasant, pleasing, regular fellow, right neighborly, sociable, social, suitable, sympathetic, well-suited
Antonyms: disagreeable, hostile, ill-suited, incompatible, uncongenial, unfriendly

Main Entry: sympathetic
Part of Speech: adjective 2
Definition: agreeable
Synonyms: amenable, appreciative, approving, companionable, compatible, congenial, congruous, consistent, consonant, cool, down, encouraging, favorably disposed, friendly, hip, like-minded, open, open-minded, pro, receptive, responsive, simpatico, tuned in, vicarious, well-disposed, well-intentioned
Antonyms: unfriendly, unsociable, unsympathetic

Main Entry: unanimous
Part of Speech: adjective
Definition: in agreement
Synonyms: accepted, accordant, agreed, agreeing, as one, assenting, collective, combined, common, communal, concerted, concordant, concurrent, consensus, consentient, consistent, consonant, harmonious, homogeneous, like-minded, popular, public, shared, single, solid, uncontested, undisputed, undivided, unified, united, universal, unquestioned
Antonyms: split

Main Entry: united
Part of Speech: adjective
Definition: combined
Synonyms: affiliated, agreed, allied, amalgamated, assembled, associated, banded, coadunate, cognate, collective, concerted, concordant, confederated, congruent, conjoint, conjugate, conjunctive, consolidated, cooperative, corporate, federal, homogeneous, hooked up, in accord, in cahoots, incorporated, integrated, joined up, leagued, like-minded, lined up, linked, one, plugged in, pooled, tied in, unanimous, undivided, unified, unitary
Antonyms: divided, separated

Ovo bi odgovaralo političkom kontekstu (Oxford, Bujas)

Definicija sa web sajta:
A fervent, sometimes militant supporter or proponent of a party, cause, faction, person, or idea.

Mislim da se u ovom konkretnom slucaju morao objasniti malo siri kontekst, jer bitno je i ko je pisao izvorni tekst, sta sledi i sta je prethodilo recenici iz primera. Vrlo verovatno je da se ovde ne misli konkretno na one prave istomišljenike u smislu onih koji slepo prate stavove stranke ili partije, nego na obične članove partije kojis u u njoj samo zbog ministarskog mesta. Ali opet kažem, bitan je širi kontekst rečenice i celog teksta.

ili fellow party men/members

ili: supporter, partner

a u politickom kontekstu:
political friend/associate