Saladin was very much a champion of Sunni Islam, to which the Fatimid Caliphate he effectively dissolved was, at least for a time, a serious rival (although the Fatimid Caliphs had very little "real power" by Saladin's time). It is worth remembering that some of his actions may have been exaggerated as a propaganda tool of Sunni Islam over its Shia rivals.

We can see some of the attitudes towards the Shia in "Bahr al-fava'id" (Sea of Precious Virtues) which was written between 1159 and 1162 (slightly before Saladin became vizier and later sultan of Egypt) in which the author writes about the Ismailis (at this point multiple different sects within Shia Islam): “There are twenty sorts of infidels, but the heretics are more infidel than any, and they are worse than the seven hundred sects of Gabrs. Shedding a heretic’s blood is the equal of seventy holy wars... Know that killing them is more lawful than rainwater; sultans and kings are required to suppress and kill them, and cleanse the earth’s back of their pollution and evil . . . It is better to shed the blood of a heretic than to kill seventy Greek infidels”

(Gabrs being Zoroastrians)

After Saladin's rise to official power he consolidated it after the death of the final Fatimid Caliph al-Adid. "Saladin imprisoned his children and kinsmen and finally caused them all to drink the draught of annihilation and utterly extinguished their race. Saladin now became supreme: his achievements were praiseworthy and the circumstances of his life are well-known" and words to this effect can be found in the works of ibn al-Athir, Juvayni and Rashid al-Din although the latter two are derivative of the former.

Saladin's own biographer Ibn Shaddad is much more vague in his account only writing that he seized "temporal power".

At the very least this can be extended to the Hafizi Ismailis (the religion of the Fatimid Caliphs of the time) although it could likely be extended to Ismailism and perhaps even Shi'ism more generally as later historians seem to use the terms "Batiniyah" (people of esotericism), "Ismailiyah", "Qaramitah" (a branch of Ismailism that were rivals to the Fatimids), "Fatimid", "Mulhid" (heretic) interchangeably.

There is also his clashes with the Assassins, themselves a different Ismaili group. This seems a little more justified as they were, generally speaking, an opposing political force who did make at least two attempts on Saladin's life. Following Saladin's unsuccessful siege at Masyaf it seems they did work together for a time against the Crusaders. However about five years after that siege Saladin wrote to the Abbasid Caliph for aid in attempting to destroy them, viewing the Assassins as as great a threat to Islam as the Franks.

Perhaps less violently he at the very least "curated" the Fatimid libraries in Egypt to remove works about Ismaili history and theology, although there are some more extreme tellings of swathes of books being burnt, buried or dumped in the Nile. However some of these were saved by Tayyibi Ismailis when they fled to India and Yemen. He also converted al-Azhar into a centre of Shafi'i Sunni learning when it had previously taught all schools and even different religions (although it did have an Ismaili bias).

In summary: Yes Saladin did take targeted violent action against the Shia population within his realm. However it is possible that some of it was exaggerated as authors saw his rise as a victory of "True Islam" over heresy and what would make us uncomfortable in the modern era was celebrated in his.

Sources:

Beben, Daniel. (2017). Remembering Saladin: The Crusades and the Politics of Heresy in Persian Historiography. Journal of the Royal Asiatic Society. 28. 1-23

Ann K. S. Lambton. (1971) “Islamic Mirrors for Princes,” Quaderno dell’Accademia Nazionale dei Lincei 160. pp. 419–442.

Bahr al-favaʾid. translated by Julie Scott Meisami as The Sea of Precious Virtues: A Medieval Islamic Mirror for Princes (Salt Lake City, 1991).

Suleiman Ali Mourad and James E. Lindsay, The Intensification and Reorientation of Sunni Jihad Ideology in the Crusader Period: Ibn ʻAsākir of Damascus (1105-1176) and His Age, with an Edition and Translation of Ibn ʻAsākir’s The Forty Hadiths for Inciting Jihad (Leiden, 2013)

ʿAta Malik Juvayni, The History of the World Conqueror, translated by John A. Boyle (Manchester, 1958), pp. 16–17

Bernard Lewis. (1953). Saladin and the Assassins. Bulletin of the School of Oriental and African Studies, 15(2), 239-245

Paul Walker, Exploring an Islamic Empire: Fatimid History and its Sources, (London, 2002).