Update!
Asked tutor #2: she says that 白い黒い何か, 長い広い所 etc are used often enough in casual speech and in speech-containing media, but that when using keigo, speaking officially, or talking with people outside of your uchi group you’d use the more formal 白くて黒い何か. Other than that, she says there’s no semantic or nuance-ic difference between the two.
In the case of 白い白い何か, she says the repetition is considered emphasis and is acceptable in formal speech.