It is ridiculous to find some trying to minimize the Umayyad role in the killing of al-Ḥusayn when it was acknowledged by the Caliph ʿAbd al-Malik b. Marwān (r. 65-86) himself.
The prolific scholar Ibn Abī Dunyā (d. 281) reports with his chain:
ʿAbd al-Malik b. Marwān used to write to (his governor) al-Ḥajjāj: “Keep me away from the blood of the Banī ʿAbd al-Muṭṭalib for I saw the Banī Ḥarb shedding it thus they were not given respite (i.e. their kingdom was taken away from them)”
حَدَّثَنَا سُلَيْمَانُ بْنُ أَبِي شَيْخٍ قَالَ: حَدَّثَنَا سُلَيْمَانُ بْنُ زِيَادٍ، عَنْ أَخِيهِ يَحْيَى بْنِ زِيَادٍ قَالَ: كَانَ عَبْدُ الْمَلِكِ بْنُ مَرْوَانَ يَكْتُبُ إِلَى الْحَجَّاجِ: جَنِّبْنِي دِمَاءَ بَنِي عَبْدِ الْمُطَّلِبِ فَإِنِّي رَأَيْتُ بَنِيَ حَرْبٍ أَصَابُوهَا فَلَمْ يُمْهِلْ لَهُمْ
Ibn Taymiyya (d. 728) accepted this report in his Minhāj al-Sunna. He writes:
“This lie is akin to the lie of the one who says ‘al-Ḥajjāj killed the ashrāf (descendants of the Prophet)’ whereas al-Ḥajjāj did not kill anyone from the Banī Hāshim despite his oppression and murder of many other than them. Instead he killed many of the Arab nobility. ʿAbd al-Malik had sent (a letter) to him that he should not kill anyone from the Banī Hāshim and noted how when al-Ḥusayn was killed during the rule of the Banī Ḥarb, that is the rule of Yazīd, evil had befallen them, so ʿAbd al-Malik took lesson from that and forbade him from killing anyone from among the Banī Hāshim …”
بَلْ هَذَا الْكَذِبُ مِثْلُ كَذِبِ مَنْ يَقُولُ: إِنَّ الْحَجَّاجَ قَتَلَ الْأَشْرَافَ، وَالْحَجَّاجُ لَمْ يَقْتُلْ أَحَدًا مِنْ بَنِي هَاشِمٍ، مَعَ ظُلْمِهِ وَفَتْكِهِ بِكَثِيرٍ مِنْ غَيْرِهِمْ، لَكِنْ قَتَلَ كَثِيرًا مِنْ أَشْرَافِ الْعَرَبِ، وَكَانَ عبد الْمَلِكُ قَدْ أَرْسَلَ إِلَيْهِ أَنْ لَا يَقْتُلَ أَحَدًا مِنْ بَنِي هَاشِمٍ، وَذَكَرَ لَهُ أَنَّهُ لَمَّا قُتِلَ الْحُسَيْنُ فِي وِلَايَةِ بَنِي حَرْبٍ - يَعْنِي مُلْكَ يَزِيدَ - أَصَابَهُمْ شَرٌّ، فَاعْتَبَرَ عَبْدُ الْمَلِكِ بِذَلِكَ، فَنَهَاهُ أَنْ يَقْتُلَ أَحَدًا مِنْ بَنِي هَاشِمٍ
Note: Ḥarb is the name of Abū Sufyān’s father and the allusion here is to Yazīd and how this branch of the Umayyads soon lost the throne after al-Ḥusayn’s killing.
Ibn Taymiyya obfuscates when he speaks of al-Ḥusayn being killed “in the rule of Yazīd” thereby shifting direct responsibility whereas ʿAbd al-Malik’s original words are much more direct when he refers to the “Banī Ḥarb shedding it (aṣābūhā)”
References: Al-Ishrāf fī Manāzil al-Ashrāf (ed. Maktabat al-Rushd), p. 255, n. 321; Minhāj al-Sunna al-Nabawiyya (ed. Muḥammad Rashād Sālim), v. 8, p. 105.