PETERS, JULIE STONE. “Staging the Last Judgment in the Trial of Charles I.” Representations, no. 143 (2018): 1–35. https://www.jstor.org/stable/26504449.

This is the best I can find in regard to perspectives of King Charles I as an idolator. If there is an account of Cromwell directly accusing Charles I of Idolatry I couldn’t find it easily.

As for the rest I found this

His destruction of idols and statues largely happened in Ireland but also occurred in England source

As for closing bars, his administration did this but not all bars, just ones that were “unlicensed and disorderly” source