Theres a mistaken assumption in your question: Yaqub ibn al-Layth did not fight mainly against the Abbasids.

The wikipedia article cites two historians: CE Bosworth and DG Tor.

While I don’t have the book by Tor that they are citing, Tor actually wrote an article on the historiography of the motivations of the Saffarids that answers your question both clearly and in great detail. https://www.jstor.org/stable/25188288?seq=1#page_scan_tab_contents

Tor makes clear that previous assertions that Yaqub was driven purely by a desire for raw power (made by Bosworth, among others) are largely without base in the primary sources. He also makes clear that almost all of Yaqub’s campaigns were against unbelievers or infidels, at least as construed by the view of a 9th century zealot like Yaqub.

He also argues that in the one campaign that Yaqub launched against the Abbasid Caliph Mutamid because, among other things, Mutamid was failing to defend Islam (this was the time of the Zanj rebellion). He also presents evidence that Yaqub was colluding with other members of the Abbasid dynasty to depose Mutamid and place another Abbasid on the throne.

All of this is presented convincingly to my reading by Tor. I recommend the full article.