The disbelief of the people of Lut along with their commission of the heinous act

Question:
Honorable Shaykh, may Allah grant you success. In Ibn al-Qayyim’s (may Allah have mercy on him) statement regarding the people of Lut, concerning their shirk (associating partners with Allah) and their kufr (disbelief), is this a refutation of those who say that the people of Lut were destroyed only for the sin of sodomy and were not mushrikin (those who associate partners with Allah)?

Answer:
Their rejection of the messengers, is that not kufr (disbelief)? This is kufr (disbelief) by scholarly consensus. So, along with their kufr (disbelief), they committed the heinous act. Yes.