The reason why its is used here is that the gerund, being, plus its constituent, the color of blood, are together treated as a noun; and this noun is modified by a possessive adjective, its. Alternatively, you could say its modifies only the head of the noun phrase, being. If you replace the gerund phrase with a regular noun of equivalent meaning, the possessive adjective is even compulsory:
It has been suggested that this reaction to red may be due to its bloody colouration.
Traditionally, the possessive was or is considered compulsory by many style books, especially with pronouns, like its. This is probably seen as correct by almost everyone. But many others would write a simple personal pronoun, it, which is considered correct by some but not by others.