This is wrong because the rules of parallel structure mean that the writer is saying ; "fur that is thickly-coloured, softly-coloured, and brightly-coloured". This doesn't make too much sense in the context of fur, especially "thickly-coloured". However, I think the writer really means: "fur that is thick, soft, and brightly-coloured."

With fur that is thick, soft, and brightly colored, the marmoset is distinguishable from other members of the mongkey family. I would only have one with "LY".

Also, the marmoset is a monkey specie, not "mongkey".

Yup, I missed that. Thanks torusan