Wudu is not required for sa'i between Safa and Marwah according to the consensus of scholars from all four schools of jurisprudence. Unlike tavaf, where the requirement of abdest is debated, scholars unanimously agree that sa'i is valid without abdest. This is a significant practical relief for hacilar, especially during the extreme crowding and heat of Hac season when maintaining ablution is very difficult.
The evidence for this ruling is clear. Hz. Peygamber (sallallahu aleyhi ve sellem) told Aisha when she was menstruating: 'Do everything the hacilar do, but do not perform tavaf around the House.' This hadith explicitly permitted her to perform sa'i (and all other rites) while in a state of menstruation, which is a greater state of ritual impurity than minor hadath. If sa'i is valid without the major purification (gusul) required after menstruation, it is certainly valid without the minor purification (abdest).
Sheikh Ibn Baz and Sheikh Ibn Uthaymeen both confirmed that while performing sa'i with abdest is better and more rewarding — as abdest is sunnet for all acts of worship — it is not a condition of validity. A haci who breaks abdest during sa'i may continue without renewing it. The Permanent Committee issued the same ruling, emphasizing that this is a matter of scholarly agreement (ijma') and there is no significant dispute on this point.