What can cause two OSPF neighbors to be stuck in the EXSTART state?

Low bandwidth slows OSPF convergence and may cause retransmissions, but it does not prevent the EXSTART state from progressing to EXCHANGE - the adjacency will eventually complete just slowly.

During the EXSTART and EXCHANGE states, OSPF routers exchange DBD packets. If the MTU values differ between neighbors, the router with the smaller MTU will receive DBD packets that exceed its MTU and silently drop them, causing the higher-MTU router to keep retransmitting and the adjacency to remain permanently stuck in EXSTART or EXCHANGE state.

Passive interfaces stop OSPF from sending Hello packets on that interface, so neighbors would never even reach INIT state, let alone get stuck in EXSTART.

Layer 1 connectivity alone (no Layer 2 or Layer 3) means OSPF Hellos cannot be exchanged at all, so the neighbor relationship would not form any OSPF state, not specifically EXSTART.