No. A period during Hajj does not mean the pilgrimage is missed or has to be abandoned. The clearest evidence for this is what happened to 'A'ishah herself during Hajjat al-Wada' (the Farewell Pilgrimage), and the instructions the Prophet (Salla Allahu 'Alayhi Wa Sallam) gave her are what scholars still apply today.
'A'ishah (Radi'Allahu Anha) had entered ihram intending Umrah, then her period began before she reached Makkah. She wept, afraid she would miss the pilgrimage that year. The Prophet (Salla Allahu 'Alayhi Wa Sallam) told her: "This is something Allah has decreed for the daughters of Adam. So do everything that the pilgrims do, except do not perform Tawaf around the House until you are pure." (Narrated by al-Bukhari and Muslim). On his instruction she wore ihram throughout, stood at Arafah, spent the night at Muzdalifah and at Mina, and threw the jamarat, all while menstruating. Only Tawaf al-Ifadah waited until she was pure.
Almost everything else in the pilgrimage follows the same pattern, since only tawaf itself requires purity from hayd:
- Entering ihram and reciting the talbiyah.
- Standing at Arafah (wuquf), the one pillar without which Hajj is not valid at all.
- Spending the night at Muzdalifah and at Mina.
- Throwing the jamarat.
- Du'a, dhikr, and reciting Qur'an, on the same difference of opinion that applies to recitation outside of Hajj, and the rest of the acts of worship that stay open during hayd apply on Hajj as anywhere else. If she wants to follow along in a printed guide or Mushaf, the rules on touching the Qur'an during hayd apply here exactly as they do at home.
What does wait for purity is Tawaf al-Ifadah, the obligatory tawaf of Hajj, together with the two rak'ahs prayed after it, and ordinarily Sa'i between Safa and Marwah, since it is performed immediately after a tawaf. She also does not enter a mosque to pray inside it while bleeding, including the Masjid al-Haram, for the same reason she would not enter any other mosque. She stays in ihram and keeps its restrictions, such as not wearing perfume and not cutting her hair or nails, until Tawaf al-Ifadah is finally performed, however many days that takes.
For most pilgrims this resolves itself: she becomes pure before her flight home, performs ghusl, then makes Tawaf al-Ifadah and Sa'i, and her Hajj is complete exactly as if her period had not happened. 'A'ishah's own case had one extra step that was specific to her, not a general rule: because the delay had folded her Umrah into a combined Hajj, the Prophet sent her, once her Hajj was finished, to a place outside the Haram called Tan'im, to enter ihram again for a separate Umrah, so that she would have performed both. That is her situation, not something every pilgrim whose period overlaps with Hajj needs to repeat.
The harder case is a pilgrim whose flight home is booked before she is likely to be pure, and this is where the schools genuinely differ, because they disagree on what purity actually is in relation to tawaf.
- The Maliki, Shafi'i, and Hanbali schools hold that purity from hayd is a shart, meaning a condition for the tawaf's validity. A tawaf performed while bleeding simply does not count. On this view, if she truly cannot delay her departure, she remains obligated to return and complete Tawaf al-Ifadah whenever she is able, since it carries no fixed deadline.
- The Hanafi school holds that purity is wajib, a strong obligation, rather than a shart, a condition for validity. On this view a tawaf performed while menstruating is valid, though blameworthy, and an expiation, traditionally a sacrificial animal, becomes due for having performed it in that state. This is the position contemporary fatwa councils most often turn to for a pilgrim who has no way to extend her stay, since it lets her leave Makkah with her Hajj actually complete rather than unfinished.
Because the decision carries real consequences and depends on her exact travel dates, this is a case worth putting to a scholar directly, ideally before she flies out if her period is due to fall around her Hajj days. Some contemporary scholars also discuss period-delaying medication as an option worth asking a doctor about in advance, precisely to avoid this situation. The same timing dilemma, and the same difference between the schools over it, applies just as directly to a standalone Umrah trip outside of Hajj season; see what if your period starts during Umrah for that case on its own.