Although the Romans didn't subscribe to 20th century racial categories ("Caucasian", "Negroid", etc), the Romans nevertheless traded in some truly crude stereotypes of non-Romans. Looking eastward, the invective became progressively more caustic. "The words of Greeks issue from their lips; those of Romans from their heart" (Plut. Cat. Mai., 12.5). Phrygians, Cicero tells us, are best improved by whipping; 'worst of the Mysians' was the ultimate insult; Carians were so worthless as to be fit only for human experiments; Cappadocians were paragons of stupidity, tastelessness, and beastliness (Cic. Flac. 65; Cic., Red. Sen., 14). Finally, Asiatic Greeks, Syrians, and Jews were born for servitude (Cic. Flac. 67, Livy 35.49.8, 36.17.4-5). Looking southward, the Punica were considered paragons of treachery, with Sardinians being so rotten that they were abandoned even by the Punica (Cic., Scaur. 42). Egyptians, of course, were animal-worshipping degenerates (Cic. Tusc. 5.78, Nat. D. 1.16.43). Looking westward, the Romans saw nothing but barbarism: Gauls and Spaniards were hairy, cruel, ferocious monsters (Cic. Font 31, 33, 41, 43-4; Cic Q Fr 1.1.27), and Spaniards brushed their teeth in piss (Catull. 37.20, 39.17-21).
Legally, all of these peoples could be admitted as citizens, it is true. However, the only gateway to citizenship was slavery. Moreover, the passage from foreign slave to free Roman--with all the rights attendant thereto--was often purchased by the slave himself, who then lived in perpetual obligation to his former master. It was a good system for Rome (until Augustus put the brakes on it), and even the Greeks admired it: Phillip V himself commended it in a letter to the Larissans (Syll. 3, 543: 29 - 34).
I think the bottom-line is that the Romans, though inclusive politically, still never doubted their superiority of other peoples, whom they showered with slurs, stereotypes, and slavery. Not exactly friendly behavior, if you ask me.