Why did Imam Malik drop Ikrimah from his narration of Thawr ibn Zayd from Ibn Abbas, if he believed that Ikrimah was not a valid authority, and why would he narrate from him at all in this case?

No text has been found from Imam Malik proving that 'Ikrimah is not an authority for him; rather, many authenticated him and used him as a source. Malik narrated from 'Ikrimah in Al-Muwatta. Ibn 'Abd al-Barr discussed the omission of 'Ikrimah from some of Al-Muwatta's chains of transmission, clarifying that Malik mentioned 'Ikrimah and explicitly named him in other places in Al-Muwatta. He also explained that the claim of his omission due to dislike is weak, especially since Malik relied on 'Ikrimah's narration in other matters, preferring it over the narrations of prominent Tabi'un.