Not abs, but core. That includes hip stabilizers, glute stabilizers, etc. All that affects controlling the ROTATION of your pelvis and spine, and rotation on the moving, swaying bike on the road is probably the big contributor to your SI joint pain. (versus a fixed position spin bike).

I used to have SI joint pain only when I got out of the saddle to climb (rotation when no saddle to fix my pelvis position).

Somebody posted this cycling core training video in the training forum recently, it is very good. The walkout band exercises she demonstrates in the second half might be particularly good for stabilizing your probable rotation issues. https://www.fundamentalvelo.com/2017...lists-artemis/