Unchained Eidolon is unable to take the Bite Evolution if it's not a Serpentine Type, evnenthough Serpentine is not part of the Unchained Rules.
This looks like a rule from the APG Summoner conflicting with the Unchained Summoner rules.
Not wholly correct. While the report is accurate in the Bite Evolution requirement does not require a Base Form of Serpentine, the Serpentine Base Form is part of the Unchained Rules. Biped, Quadruped and Serpentine all exist on page 34. The one Base Form not present is Aquatic.
Bite: Requirements: Agathion, daemon, demon,
devil, div, elemental, protean, or psychopomp subtype.
Mount (Ex): The eidolon is properly skilled and formed
to serve as a combat-trained mount. The eidolon must be
at least one size category larger than its rider. Requirements:
Daemon, demon, devil, elemental, or protean subtype;
quadruped or serpentine base form.